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BEGIN:VEVENT
SUMMARY:Chris Bowman (University of Kent)
DTSTART;VALUE=DATE-TIME:20200915T073000Z
DTEND;VALUE=DATE-TIME:20200915T083000Z
DTSTAMP;VALUE=DATE-TIME:20220816T031724Z
UID:OISTRTS/1
DESCRIPTION:Title:
Tautological p-Kazhdan–Lusztig Theory for cyclotomic Hecke algebras\
nby Chris Bowman (University of Kent) as part of OIST representation theor
y seminar\n\n\nAbstract\nWe discuss a new explicit isomorphism between (tr
uncations of) quiver Hecke algebras and Elias–Williamson’s diagrammati
c endomorphism algebras of Bott–Samelson bimodules. This allows us to de
duce that the decomposition numbers of these algebras (including as exampl
es the symmetric groups and generalised blob algebras) are tautologically
equal to the associated p-Kazhdan–Lusztig polynomials\, provided that th
e characteristic is greater than the Coxeter number. This allows us to giv
e an elementary and explicit proof of the main theorem of Riche–Williams
on’s recent monograph and extend their categorical equivalence to cyclot
omic Hecke algebras\, thus solving Libedinsky–Plaza’s categorical blob
conjecture.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mahir Can (Tulane University)
DTSTART;VALUE=DATE-TIME:20200929T000000Z
DTEND;VALUE=DATE-TIME:20200929T010000Z
DTSTAMP;VALUE=DATE-TIME:20220816T031724Z
UID:OISTRTS/2
DESCRIPTION:Title:
Spherical Varieties and Combinatorics\nby Mahir Can (Tulane University
) as part of OIST representation theory seminar\n\n\nAbstract\nLet G be a
reductive complex algebraic group with a Borel subgroup B. A spherical G-v
ariety is an irreducible normal G-variety X where B has an open orbit. If
X is affine\, or if it is projective but endowed with a G-linearized ample
line bundle\, then the group action criteria for the sphericality is in f
act equivalent to the representation theoretic statement that a certain sp
ace of functions (related to X) is multiplicity-free as a G-module. In thi
s talk\, we will discuss the following question about a class of spherical
varieties: if X is a Schubert variety for G\, then when do we know that X
is a spherical L-variety\, where L is the stabilizer of X in G.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eoghan McDowell (Royal Holloway\, University of London)
DTSTART;VALUE=DATE-TIME:20201013T073000Z
DTEND;VALUE=DATE-TIME:20201013T083000Z
DTSTAMP;VALUE=DATE-TIME:20220816T031724Z
UID:OISTRTS/3
DESCRIPTION:Title:
The image of the Specht module under the inverse Schur functor\nby Eog
han McDowell (Royal Holloway\, University of London) as part of OIST repre
sentation theory seminar\n\n\nAbstract\nThe Schur functor and its inverses
give an important connection between the representation theories of the s
ymmetric group and the general linear group. Kleshchev and Nakano proved i
n 2001 that when the characteristic of the field is at least 5\, the image
of the Specht module under the inverse Schur functor is isomorphic to the
dual Weyl module. In this talk I will address what happens in characteris
tics 2 and 3: in characteristic 3\, the isomorphism holds\, and I will giv
e an elementary proof of this fact which covers also all characteristics o
ther than 2\; in characteristic 2\, the isomorphism does not hold for all
Specht modules\, and I will classify those for which it does. Our approach
is with Young tableaux\, tabloids and Garnir relations.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rob Muth (Washington and Jefferson College)
DTSTART;VALUE=DATE-TIME:20201027T000000Z
DTEND;VALUE=DATE-TIME:20201027T010000Z
DTSTAMP;VALUE=DATE-TIME:20220816T031724Z
UID:OISTRTS/4
DESCRIPTION:Title:
Specht modules and cuspidal ribbon tableaux\nby Rob Muth (Washington a
nd Jefferson College) as part of OIST representation theory seminar\n\n\nA
bstract\nRepresentation theory of Khovanov-Lauda-Rouquier (KLR) algebras i
n affine type A can be studied through the lens of Specht modules\, associ
ated with the cellular structure of cyclotomic KLR algebras\, or through t
he lens of cuspidal modules\, associated with categorified PBW bases for t
he quantum group of affine type A. Cuspidal ribbons provide a sort of comb
inatorial bridge between these approaches. I will describe some recent res
ults on cuspidal ribbon tableaux\, and some implications in the world of K
LR representation theory\, such as bounds on labels of simple factors of S
pecht modules\, and the presentation of cuspidal modules. Portions of this
talk are joint work with Dina Abbasian\, Lena Difulvio\, Gabrielle Paster
nak\, Isabella Sholtes\, and Frances Sinclair.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jieru Zhu (Hausdorff Institute of Mathematics)
DTSTART;VALUE=DATE-TIME:20201110T073000Z
DTEND;VALUE=DATE-TIME:20201110T083000Z
DTSTAMP;VALUE=DATE-TIME:20220816T031724Z
UID:OISTRTS/5
DESCRIPTION:Title:
Double centralizer properties for the Drinfeld double of the Taft algebras
\nby Jieru Zhu (Hausdorff Institute of Mathematics) as part of OIST re
presentation theory seminar\n\n\nAbstract\nThe Drinfeld double of the taft
algebra\, $D_n$\, whose ground field contains $n$-th roots of unity\, has
a known list of 2-dimensional irreducible modules. For each of such modul
e $V$\, we show that there is a well-defined action of the Temperley-Lieb
algebra $TL_k$ on the $k$-fold tensor product of $V$\, and this action com
mutes with that of $D_n$. When $V$ is self-dual and when $k \\leq 2(n-1)$\
, we further establish a isomorphism between the centralizer algebra of $D
_n$ on $V^{\\otimes k}$\, and $TL_k$. Our inductive argument uses a rank
function on the TL diagrams\, which is compatible with the nesting functio
n introduced by Russell-Tymoczko. This is joint work with Georgia Benkart\
, Rekha Biswal\, Ellen Kirkman and Van Nguyen.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qi Wang (Osaka University)
DTSTART;VALUE=DATE-TIME:20201117T073000Z
DTEND;VALUE=DATE-TIME:20201117T083000Z
DTSTAMP;VALUE=DATE-TIME:20220816T031724Z
UID:OISTRTS/6
DESCRIPTION:Title:
On $\\tau$-tilting finiteness of Schur algebras\nby Qi Wang (Osaka Uni
versity) as part of OIST representation theory seminar\n\n\nAbstract\nSupp
ort $\\tau$-tilting modules are introduced by Adachi\, Iyama and Reiten in
2012 as a generalization of classical tilting modules. One of the importa
nce of these modules is that they are bijectively corresponding to many ot
her objects\, such as two-term silting complexes and left finite semibrick
s. Let $V$ be an $n$-dimensional vector space over an algebraically closed
field $\\mathbb{F}$ of characteristic $p$. Then\, the Schur algebra $S(n\
,r)$ is defined as the endomorphism ring $\\mathsf{End}_{\\mathbb{F}G_r}\\
left ( V^{\\otimes r} \\right )$ over the group algebra $\\mathbb{F}G_r$
of the symmetric group $G_r$. In this talk\, we discuss when the Schur alg
ebra $S(n\,r)$ has only finitely many pairwise non-isomorphic basic suppor
t $\\tau$-tilting modules.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Jacon (University of Reims Champagne-Ardenne)
DTSTART;VALUE=DATE-TIME:20201208T073000Z
DTEND;VALUE=DATE-TIME:20201208T083000Z
DTSTAMP;VALUE=DATE-TIME:20220816T031724Z
UID:OISTRTS/7
DESCRIPTION:Title:
Cores of Ariki-Koike algebras\nby Nicolas Jacon (University of Reims C
hampagne-Ardenne) as part of OIST representation theory seminar\n\n\nAbstr
act\nWe study a natural generalization of the notion of cores for l-partit
ions: the (e\, s)-cores. We relate this notion with the notion of weight a
s defined by Fayers and use it to describe the blocks of Ariki-Koike algeb
ras.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Fayers (Queen Mary University of London)
DTSTART;VALUE=DATE-TIME:20210112T073000Z
DTEND;VALUE=DATE-TIME:20210112T083000Z
DTSTAMP;VALUE=DATE-TIME:20220816T031724Z
UID:OISTRTS/8
DESCRIPTION:Title:
The Mullineux map\nby Matthew Fayers (Queen Mary University of London)
as part of OIST representation theory seminar\n\n\nAbstract\nIn character
istic p\, the simple modules for the symmetric group \\(S_n\\) are the Jam
es modules \\(D^\\lambda\\)\, labelled by p-regular partitions of n. If we
let \\(sgn\\) denote the 1-dimensional sign module\, then for any p-regul
ar \\(\\lambda\\)\, the module \\(D^\\lambda\\otimes sgn\\) is also a simp
le module. So there is an involutory bijection \\(m_p\\) on the set of p-r
egular partitions such that \\(D^\\lambda\\otimes sgn=D^{m_p(\\lambda)}\\)
. The map \\(m_p\\) is called the Mullineux map\, and an important problem
is to describe \\(m_p\\) combinatorially. There are now several known sol
utions to this problem. I will describe the history of this problem and ex
plain the known combinatorial solutions\, and then give a new solution bas
ed on crystals and regularisation.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Chung (Okinawa Institute of Science and Technology)
DTSTART;VALUE=DATE-TIME:20210126T073000Z
DTEND;VALUE=DATE-TIME:20210126T083000Z
DTSTAMP;VALUE=DATE-TIME:20220816T031724Z
UID:OISTRTS/9
DESCRIPTION:Title:
\\(\\imath\\)Quantum Covering Groups: Serre presentation and canonical bas
is\nby Chris Chung (Okinawa Institute of Science and Technology) as pa
rt of OIST representation theory seminar\n\n\nAbstract\nIn 2016\, Bao and
Wang developed a general theory of canonical basis for quantum symmetric p
airs \\((\\mathbf{U}\, \\mathbf{U}^\\imath)\\)\, generalizing the canonica
l basis of Lusztig and Kashiwara for quantum groups and earning them the 2
020 Chevalley Prize in Lie Theory. The \\(\\imath\\)divided powers are pol
ynomials in a single generator that generalize Lusztig's divided powers\,
which are monomials. They can be similarly perceived as canonical basis in
rank one\, and have closed form expansion formulas\, established by Berma
n and Wang\, that were used by Chen\, Lu and Wang to give a Serre presenta
tion for coideal subalgebras \\(\\mathbf{U}^\\imath\\)\, featuring novel \
\(\\imath\\)Serre relations when \\(\\tau(i) = i\\).\n\nQuantum covering g
roups\, developed by Clark\, Hill and Wang\, are a generalization that `co
vers' both the Lusztig quantum group and quantum supergroups of anisotropi
c type. In this talk\, I will talk about how the results for \\(\\imath\\)
-divided powers and the Serre presentation can be extended to the quantum
covering algebra setting\, and subsequently applications to canonical basi
s for \\(\\mathbf{U}^\\imath_\\pi\\)\, the quantum covering analogue of \\
(\\mathbf{U}^\\imath\\)\, and quantum covering groups at roots of 1.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Davidson (Reed College)
DTSTART;VALUE=DATE-TIME:20210216T003000Z
DTEND;VALUE=DATE-TIME:20210216T013000Z
DTSTAMP;VALUE=DATE-TIME:20220816T031724Z
UID:OISTRTS/10
DESCRIPTION:Title: Type P Webs and Howe Duality\nby Nick Davidson (Reed College) as part
of OIST representation theory seminar\n\n\nAbstract\nWebs are combinatori
ally defined diagrams which encode homomorphisms between tensor products o
f certain representations of Lie (super)algebras. I will describe some re
cent work with Jon Kujawa and Rob Muth which defines webs for the type P L
ie superalgebra\, and then uses these webs to deduce an analog of Howe dua
lity for this Lie superalgebra.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Yi Rui Low (National University of Singapore)
DTSTART;VALUE=DATE-TIME:20210302T073000Z
DTEND;VALUE=DATE-TIME:20210302T083000Z
DTSTAMP;VALUE=DATE-TIME:20220816T031724Z
UID:OISTRTS/11
DESCRIPTION:Title: Adjustment matrices\nby Aaron Yi Rui Low (National University of Sing
apore) as part of OIST representation theory seminar\n\n\nAbstract\nJames'
s Conjecture predicts that the adjustment matrix for weight $w$ blocks of
the Iwahori-Hecke algebras $\\mathcal{H}_{n}$ and the $q$-Schur algebras $
\\mathcal{S}_{n}$ is the identity matrix when $w<\\textnormal{char}(\\math
bb{F})$. Fayers has proved James's Conjecture for blocks of $\\mathcal{H}_
{n}$ of weights 3 and 4. We shall discuss some results on adjustment matri
ces that have been used to prove James's Conjecture for blocks of $\\mathc
al{S}_{n}$ of weights 3 and 4 in an upcoming paper. If time permits\, we w
ill look at a proof of the weight 3 case.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Kleshchev (University of Oregon)
DTSTART;VALUE=DATE-TIME:20210330T003000Z
DTEND;VALUE=DATE-TIME:20210330T013000Z
DTSTAMP;VALUE=DATE-TIME:20220816T031724Z
UID:OISTRTS/12
DESCRIPTION:Title: Irreducible restrictions from symmetric groups to subgroups\nby Alexa
nder Kleshchev (University of Oregon) as part of OIST representation theor
y seminar\n\n\nAbstract\nWe motivate\, discuss history of\, and present a
solution to the following problem: describe pairs (G\,V) where V is an irr
educible representation of the symmetric group S_n of dimension >1 and G i
s a subgroup of S_n such that the restriction of V to G is irreducible. We
do the same with the alternating group A_n in place of S_n. \nThe latest
results on the problem are joint with Pham Huu Tiep and Lucia Morotti.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alistair Savage (University of Ottawa)
DTSTART;VALUE=DATE-TIME:20210202T003000Z
DTEND;VALUE=DATE-TIME:20210202T013000Z
DTSTAMP;VALUE=DATE-TIME:20220816T031724Z
UID:OISTRTS/13
DESCRIPTION:Title: Affinization of monoidal categories\nby Alistair Savage (University o
f Ottawa) as part of OIST representation theory seminar\n\n\nAbstract\nWe
define the affinization of an arbitrary monoidal category\, corresponding
to the category of string diagrams on the cylinder. We also give an alter
native characterization in terms of adjoining dot generators to the catego
ry. The affinization formalizes and unifies many constructions appearing
in the literature. We describe a large number of examples coming from Hec
ke-type algebras\, braids\, tangles\, and knot invariants.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Catharina Stroppel (University of Bonn)
DTSTART;VALUE=DATE-TIME:20210316T073000Z
DTEND;VALUE=DATE-TIME:20210316T083000Z
DTSTAMP;VALUE=DATE-TIME:20220816T031724Z
UID:OISTRTS/14
DESCRIPTION:Title: Verlinde rings and DAHA actions\nby Catharina Stroppel (University of
Bonn) as part of OIST representation theory seminar\n\n\nAbstract\nIn thi
s talk we will briefly recall how quantum groups at roots give rise Verlin
de algebras which can be realised as Grothendieck rings of certain monoida
l categories. The ring structure is quite interesting and was very much st
udied in type A. I will try to explain how one gets a natural action of ce
rtain double affine Hecke algebras and show how known properties of these
rings can be deduced from this action and in which sense modularity of the
tensor category is encoded.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Wildon (Royal Holloway\, University of London)
DTSTART;VALUE=DATE-TIME:20210427T073000Z
DTEND;VALUE=DATE-TIME:20210427T083000Z
DTSTAMP;VALUE=DATE-TIME:20220816T031724Z
UID:OISTRTS/15
DESCRIPTION:Title: Plethysms\, polynomial representations of linear groups and Hermite recip
rocity over an arbitrary field\nby Mark Wildon (Royal Holloway\, Unive
rsity of London) as part of OIST representation theory seminar\n\n\nAbstra
ct\nLet \\(E\\) be a \\(2\\)-dimensional vector space. Over the complex nu
mbers the irreducible polynomial representations of the special linear gro
up \\(SL(E)\\) are the symmetric powers \\(Sym^r E\\). Composing polynomia
l representations\, for example to form \\(Sym^4 Sym^2 E\\)\, corresponds
to the plethysm product on symmetric functions. Expressing such a plethysm
as a linear combination of Schur functions has been identified by Richard
Stanley as one of the fundamental open problems in algebraic combinatoric
s. In my talk I will use symmetric functions to prove some classical isomo
rphisms\, such as Hermite reciprocity \\(Sym^m Sym^r E \\cong Sym^r Sym^m
E\\)\, and some others discovered only recently in joint work with Rowena
Paget. I will then give an overview of new results showing that\, provided
suitable dualities are introduced\, Hermite reciprocity holds over arbitr
ary fields\; certain other isomorphisms (we can prove) have no modular gen
eralization. The final part is joint work with my Ph.D student Eoghan McDo
well.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stacey Law (University of Cambridge)
DTSTART;VALUE=DATE-TIME:20210413T073000Z
DTEND;VALUE=DATE-TIME:20210413T083000Z
DTSTAMP;VALUE=DATE-TIME:20220816T031724Z
UID:OISTRTS/16
DESCRIPTION:Title: Sylow branching coefficients and a conjecture of Malle and Navarro\nb
y Stacey Law (University of Cambridge) as part of OIST representation theo
ry seminar\n\n\nAbstract\nThe relationship between the representation theo
ry of a finite group and that of its Sylow subgroups is a key area of inte
rest. For example\, recent results of Malle–Navarro and Navarro–Tiep
–Vallejo have shown that important structural properties of a finite gro
up \\(G\\) are controlled by the permutation character \\(\\mathbb{1}_P\\b
ig\\uparrow^G\\)\, where \\(P\\) is a Sylow subgroup of \\(G\\) and \\(\\m
athbb{1}_P\\) denotes the trivial character of \\(P\\). We introduce so-ca
lled Sylow branching coefficients for symmetric groups to describe multipl
icities associated with these induced characters\, and as an application c
onfirm a prediction of Malle and Navarro from 2012\, in joint work with E.
Giannelli\, J. Long and C. Vallejo.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Max Gurevich (Technion)
DTSTART;VALUE=DATE-TIME:20210528T073000Z
DTEND;VALUE=DATE-TIME:20210528T083000Z
DTSTAMP;VALUE=DATE-TIME:20220816T031724Z
UID:OISTRTS/17
DESCRIPTION:Title: New constructions for irreducible representations in monoidal categories
of type A\nby Max Gurevich (Technion) as part of OIST representation t
heory seminar\n\n\nAbstract\nOne ever-recurring goal of Lie theory is the
quest for effective and elegant descriptions of collections of simple obje
cts in categories of interest. A cornerstone feat achieved by Zelevinsky i
n that regard\, was the combinatorial explication of the Langlands classif
ication for smooth irreducible representations of p-adic GL_n. It was a fo
rerunner for an exploration of similar classifications for various categor
ies of similar nature\, such as modules over affine Hecke algebras or quan
tum affine algebras\, to name a few. \nA next step - reaching an effective
understanding of all reducible finite-length representations remains larg
ely a difficult task throughout these settings.\n\nRecently\, joint with E
rez Lapid\, we have revisited the original Zelevinsky setting by suggestin
g a refined construction of all irreducible representations\, with the hop
e of shedding light on standing decomposition problems. This construction
applies the Robinson-Schensted-Knuth transform\, while categorifying the d
eterminantal Doubilet-Rota-Stein basis for matrix polynomial rings appeari
ng in invariant theory.\nIn this talk\, I would like to introduce the new
construction into the setting of modules over quiver Hecke (KLR) algebras.
In type A\, this category may be viewed as a quantization/gradation of th
e category of representations of p-adic groups. I will explain how adoptin
g that point of view and exploiting recent developments in the subject (su
ch as the normal sequence notion of Kashiwara-Kim) brings some conjectural
properties of the RSK construction (back in the p-adic setting) into reso
lution.\nTime permits\, I will discuss the relevance of the RSK constructi
on to the representation theory of cyclotomic Hecke algebras.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sira Gratz (University of Glasgow)
DTSTART;VALUE=DATE-TIME:20210615T073000Z
DTEND;VALUE=DATE-TIME:20210615T083000Z
DTSTAMP;VALUE=DATE-TIME:20220816T031724Z
UID:OISTRTS/18
DESCRIPTION:Title: Grassmannians\, Cluster Algebras and Hypersurface Singularities\nby S
ira Gratz (University of Glasgow) as part of OIST representation theory se
minar\n\n\nAbstract\nGrassmannians are objects of great combinatorial and
geometric beauty\, which arise in myriad contexts. Their coordinate rings
serve as a classical example of cluster algebras\, as introduced by Fomin
and Zelevinsky at the start of the millennium\, and their combinatorics is
intimately related to algebraic and geometric concepts such as to represe
ntations of algebras and hypersurface singularities. At the core lies the
idea of generating an object from a so-called “cluster” via the concep
t of “mutation”. \n\nIn this talk\, we offer an overview of Grassmanni
an combinatorics in a cluster theoretic framework\, and ultimately take th
em to the limit to explore the a priori simple question: What happens if w
e allow infinite clusters? We introduce the notion of a cluster algebra of
infinite rank (based on joint work with Grabowski)\, and of a Grassmannia
n category of infinite rank (based on joint work with August\, Cheung\, Fa
ber and Schroll).\n
LOCATION:https://researchseminars.org/talk/OISTRTS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diego Millan Berdasco (Queen Mary University of London)
DTSTART;VALUE=DATE-TIME:20210706T073000Z
DTEND;VALUE=DATE-TIME:20210706T083000Z
DTSTAMP;VALUE=DATE-TIME:20220816T031724Z
UID:OISTRTS/19
DESCRIPTION:Title: On the computation of decomposition numbers of the symmetric group\nb
y Diego Millan Berdasco (Queen Mary University of London) as part of OIST
representation theory seminar\n\n\nAbstract\nThe most important open probl
em in the modular representation theory of the symmetric group is finding
the multiplicity of the simple modules as composition factors of the Spech
t modules. In characteristic 0 the Specht modules are just the simple modu
les of the symmetric group algebra\, but in positive characteristic they m
ay no longer be simple. We will survey the rich interplay between represen
tation theory and combinatorics of integer partitions\, review a number of
results in the literature which allow us to compute composition series fo
r certain infinite families of Specht modules from a finite subset of them
\, and discuss the extension of these techniques to other Specht modules.\
n
LOCATION:https://researchseminars.org/talk/OISTRTS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hankyung Ko (Uppsala University)
DTSTART;VALUE=DATE-TIME:20210928T073000Z
DTEND;VALUE=DATE-TIME:20210928T083000Z
DTSTAMP;VALUE=DATE-TIME:20220816T031724Z
UID:OISTRTS/20
DESCRIPTION:Title: Bruhat orders and Verma modules\nby Hankyung Ko (Uppsala University)
as part of OIST representation theory seminar\n\n\nAbstract\nThe Bruhat or
der on a Weyl group has a representation theoretic interpretation in terms
of Verma modules. The talk concerns resulting interactions between combin
atorics and homological algebra. I will present several questions around t
he above realization of the Bruhat order and answer them based on a series
of recent works\, partly joint with Volodymyr Mazorchuk and Rafael Mrden.
\n
LOCATION:https://researchseminars.org/talk/OISTRTS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Wedrich (University of Hamburg)
DTSTART;VALUE=DATE-TIME:20211012T060000Z
DTEND;VALUE=DATE-TIME:20211012T070000Z
DTSTAMP;VALUE=DATE-TIME:20220816T031724Z
UID:OISTRTS/21
DESCRIPTION:Title: Knots and quivers\, HOMFLYPT and DT\nby Paul Wedrich (University of H
amburg) as part of OIST representation theory seminar\n\n\nAbstract\nI wil
l describe a surprising connection between the colored HOMFLY-PT polynomia
ls of knots and the motivic Donaldson-Thomas invariants of certain symmetr
ic quivers\, which was conjectured by Kucharski-Reineke-Stosic-Sulkowski.
I will outline a proof of this correspondence for arborescent links via qu
ivers associated with 4-ended tangles. Finally\, I will speculate about ho
w much of the HOMFLY-PT skein theory might carry over to the realm of DT q
uiver invariants and what kind of geometric information about knots might
be encoded in these quivers. This is joint work with Marko Stosic.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tianyuan Xu (University of Colorado at Boulder)
DTSTART;VALUE=DATE-TIME:20211130T003000Z
DTEND;VALUE=DATE-TIME:20211130T013000Z
DTSTAMP;VALUE=DATE-TIME:20220816T031724Z
UID:OISTRTS/22
DESCRIPTION:Title: On Kazhdan–Lusztig cells of a-value 2\nby Tianyuan Xu (University o
f Colorado at Boulder) as part of OIST representation theory seminar\n\n\n
Abstract\nThe Kazhdan–Lusztig (KL) cells of a Coxeter group are subsets
of the group defined using the KL basis of the associated Iwahori–Hecke
algebra. The cells of symmetric groups can be computed via the Robinson–
Schensted correspondence\, but for general Coxeter groups combinatorial de
scriptions of KL cells are largely unknown except for cells of a-value 0 o
r 1\, where a refers to an N-valued function defined by Lusztig that is co
nstant on each cell. In this talk\, we will report some recent progress on
KL cells of a-value 2. In particular\, we classify Coxeter groups with fi
nitely many elements of a-value 2\, and for such groups we characterize an
d count all cells of a-value 2 via certain posets called heaps. We will al
so mention some applications of these results for cell modules. This is jo
int work with Richard Green.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Seelinger (University of Michigan)
DTSTART;VALUE=DATE-TIME:20211026T003000Z
DTEND;VALUE=DATE-TIME:20211026T013000Z
DTSTAMP;VALUE=DATE-TIME:20220816T031724Z
UID:OISTRTS/23
DESCRIPTION:Title: Diagonal harmonics and shuffle theorems\nby George Seelinger (Univers
ity of Michigan) as part of OIST representation theory seminar\n\n\nAbstra
ct\nThe Shuffle Theorem\, conjectured by Haglund\, Haiman\, Loehr\, Remmel
and Ulyanov\, and proved by Carlsson and Mellit\, describes the character
istic of the $S_n$-module of diagonal harmonics as a weight generating fun
ction over labeled Dyck paths under a line with slope −1. The Shuffle Th
eorem has been generalized in many different directions\, producing a numb
er of theorems and conjectures. We provide a generalized shuffle theorem f
or paths under any line with negative slope using different methods from p
revious proofs of the Shuffle Theorem. In particular\, our proof relies on
showing a "stable" shuffle theorem in the ring of virtual GL_l-characters
. Furthermore\, we use our techniques to prove the Extended Delta Conjectu
re\, yet another generalization of the original Shuffle Conjecture.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arik Wilbert (University of South Alabama)
DTSTART;VALUE=DATE-TIME:20211109T003000Z
DTEND;VALUE=DATE-TIME:20211109T013000Z
DTSTAMP;VALUE=DATE-TIME:20220816T031724Z
UID:OISTRTS/24
DESCRIPTION:Title: Real Springer fibers and odd arc algebras\nby Arik Wilbert (Universit
y of South Alabama) as part of OIST representation theory seminar\n\n\nAbs
tract\nArc algebras were introduced by Khovanov in a successful attempt to
lift the quantum sl2 Reshetikhin-Turaev invariant for tangles to a homolo
gical invariant. When restricted to knots and links\, Khovanov’s homolog
y theory categorifies the Jones polynomial. Ozsváth-Rasmussen-Szabó disc
overed a different categorification of the Jones polynomial called odd Kho
vanov homology. Recently\, Naisse-Putyra were able to extend odd Khovanov
homology to tangles using so-called odd arc algebras which were originally
constructed by Naisse-Vaz. The goal of this talk is to discuss a geometri
c approach to understanding odd arc algebras and odd Khovanov homology usi
ng Springer fibers over the real numbers. This is joint work with J. N. Eb
erhardt and G. Naisse.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Creedon (City\, University of London)
DTSTART;VALUE=DATE-TIME:20211116T073000Z
DTEND;VALUE=DATE-TIME:20211116T083000Z
DTSTAMP;VALUE=DATE-TIME:20220816T031724Z
UID:OISTRTS/25
DESCRIPTION:Title: Defining an Affine Partition Algebra\nby Samuel Creedon (City\, Unive
rsity of London) as part of OIST representation theory seminar\n\n\nAbstra
ct\nIn this talk we motivate the construction of a new algebra called the
affine partition algebra. We summarise some of its basic properties and de
scribe an action which extends the Schur-Weyl duality between the symmetri
c group and partition algebra. We establish connections to the affine part
ition category defined recently by Brundan and Vargas and show that such a
category is a full subcategory of the Heisenberg category.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joanna Meinel (Federal Office for Information Security\, Bonn)
DTSTART;VALUE=DATE-TIME:20211214T073000Z
DTEND;VALUE=DATE-TIME:20211214T083000Z
DTSTAMP;VALUE=DATE-TIME:20220816T031724Z
UID:OISTRTS/26
DESCRIPTION:Title: Decompositions of tensor products: Highest weight vectors from branching<
/a>\nby Joanna Meinel (Federal Office for Information Security\, Bonn) as
part of OIST representation theory seminar\n\n\nAbstract\nWe consider tens
or powers of the natural sl_n-representation\, and we look for description
s of highest weight vectors therein: We discuss explicit formulas for n=2\
, a recursion for n=3\, and for bigger n we demonstrate how Jucys-Murphy e
lements allow us to compute highest weight vectors (both in theory and in
practice using sage). This is joint work with Pablo Zadunaisky.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Tubbenhauer (University of Sydney)
DTSTART;VALUE=DATE-TIME:20220201T073000Z
DTEND;VALUE=DATE-TIME:20220201T083000Z
DTSTAMP;VALUE=DATE-TIME:20220816T031724Z
UID:OISTRTS/27
DESCRIPTION:Title: On weighted KLRW algebras\nby Daniel Tubbenhauer (University of Sydne
y) as part of OIST representation theory seminar\n\n\nAbstract\nWeighted K
LRW algebras are diagram algebras that depend on continuous \nparameters.
Varying these parameters gives a way to interpolate between \nvarious alge
bras that appear in (categorical) representation theory \nsuch as semisimp
le algebras\, KLR algebras\, quiver Schur algebras and diagrammatic Chered
nik algebras.\n\nThis talk is a friendly (and diagrammatic!) introduction
explaining these algebras\, with no prior knowledge about any of these ass
umed.\n\nBased on joint work A. Mathas.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Spencer (University of Cambridge)
DTSTART;VALUE=DATE-TIME:20220301T073000Z
DTEND;VALUE=DATE-TIME:20220301T083000Z
DTSTAMP;VALUE=DATE-TIME:20220816T031724Z
UID:OISTRTS/28
DESCRIPTION:Title: (Some) Gram Determinants for \\(A_n\\) nets\nby Robert Spencer (Unive
rsity of Cambridge) as part of OIST representation theory seminar\n\n\nAbs
tract\nThe nets giving a diagrammatic description of the category of (tens
or products of) fundamental representations of \\(sl_n\\) form a cellular
category. We can then ask about the natural inner form on certain cell mod
ules. In this talk\, we will calculate the determinant of some of these fo
rms in terms of certain traces of clasps or magic weave elements (for whic
h there is a conjectured formula due to Elias). The method appears moderat
ely general and gives a result which is hopefully illuminating and applica
ble to other monoidal\, cellular categories.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Murray (Maynooth University)
DTSTART;VALUE=DATE-TIME:20220322T073000Z
DTEND;VALUE=DATE-TIME:20220322T083000Z
DTSTAMP;VALUE=DATE-TIME:20220816T031724Z
UID:OISTRTS/29
DESCRIPTION:Title: A Schur-positivity conjecture inspired by the Alperin-Mckay conjecture\nby John Murray (Maynooth University) as part of OIST representation the
ory seminar\n\n\nAbstract\nThe McKay conjecture asserts that a finite grou
p has the same number of odd degree irreducible characters as the normaliz
er of a Sylow 2-subgroup. The Alperin-McKay (A-M) conjecture generalizes t
his to the height-zero characters in 2-blocks.\n\nIn his original paper\,
McKay already showed that his conjecture holds for the finite symmetric gr
oups S_n. In 2016\, Giannelli\, Tent and the speaker established a canonic
al bijection realising A-M for S_n\; the height-zero irreducible character
s in a 2-block are naturally parametrized by tuples of hooks whose lengths
are certain powers of 2\, and this parametrization is compatible with res
triction to an appropriate 2-local subgroup.\n\nNow corresponding to a 2-b
lock of the symmetric group S_n\, there is a 2-block of a maximal Young su
bgroup of S_n of the same weight. An obvious question is whether our canon
ical bijection is compatible with restriction of height-zero characters be
tween these blocks.\n\nAttempting to prove this compatibility lead me to f
ormulate a conjecture asserting the Schur-positivity of certain difference
s of skew-Schur functions. The corresponding skew-shapes have triangular i
nner-shape\, but otherwise do not refer to the 2-modular theory. I will de
scribe my conjecture and give positive evidence in its favour.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephen Doty (Loyola University Chicago)
DTSTART;VALUE=DATE-TIME:20220215T003000Z
DTEND;VALUE=DATE-TIME:20220215T013000Z
DTSTAMP;VALUE=DATE-TIME:20220816T031724Z
UID:OISTRTS/30
DESCRIPTION:Title: Schur-Weyl duality for braid and twin groups via the Burau representation
\nby Stephen Doty (Loyola University Chicago) as part of OIST represen
tation theory seminar\n\n\nAbstract\nThe natural permutation representatio
n of the symmetric group admits a q-analogue known as the Burau representa
tion. The symmetric group admits two natural covering groups: the braid gr
oup of Artin and the twin group of Khovanov\, obtained respectively by for
getting the cubic and quadratic relations in the Coxeter presentation of t
he symmetric group. By computing centralizers of tensor powers of the Bura
u representation\, we obtain new instances of Schur-Weyl duality for braid
groups and twin groups\, in terms of the partial permutation and partial
Brauer algebras. The method produces many representations of each group th
at can be understood combinatorially. (This is joint work with Tony Giaqui
nto.)\n
LOCATION:https://researchseminars.org/talk/OISTRTS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kay Jin Lim (Nanyang Technological University)
DTSTART;VALUE=DATE-TIME:20220420T073000Z
DTEND;VALUE=DATE-TIME:20220420T083000Z
DTSTAMP;VALUE=DATE-TIME:20220816T031724Z
UID:OISTRTS/31
DESCRIPTION:Title: Descent Algebra of Type A\nby Kay Jin Lim (Nanyang Technological Univ
ersity) as part of OIST representation theory seminar\n\n\nAbstract\nFor a
finite Coxeter group W\, L. Solomon defined certain subalgebra of the gro
up algebra kW which is now commonly known as the Solomon’s descent algeb
ra. As usual\, the type A and B cases have special interest for both the a
lgebraists and combinatorists. In this talk\, I will be particularly focus
ing on the type A and modular case. It is closely related to the represent
ation theory of the symmetric group and the (higher) Lie representations.\
n
LOCATION:https://researchseminars.org/talk/OISTRTS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dean Yates (Queen Mary University of London)
DTSTART;VALUE=DATE-TIME:20220405T073000Z
DTEND;VALUE=DATE-TIME:20220405T083000Z
DTSTAMP;VALUE=DATE-TIME:20220816T031724Z
UID:OISTRTS/32
DESCRIPTION:Title: Spin representations of the symmetric group\nby Dean Yates (Queen Mar
y University of London) as part of OIST representation theory seminar\n\n\
nAbstract\nSpin representations of the symmetric group S_n can be thought
of equivalently as either projective representations of S_n\, or as linear
representations of a double cover S_n^{+} of S_n. Whilst the line
ar representation theory of S_n is dictated by removing ‘rim-hooks’ fr
om (the Young diagrams of) partitions of n\, the projective representation
theory of S_n is controlled by removing ‘bars’ from bar partitions of
n (i.e. partitions of n into distinct parts). We will look at some combin
atorial results on bar partitions from a recent paper of the author before
discussing methods for determining the modular decomposition of spin repr
esentations over fields of positive characteristic.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shinsuke Tsuchioka (Tokyo Institute of Technology)
DTSTART;VALUE=DATE-TIME:20220614T073000Z
DTEND;VALUE=DATE-TIME:20220614T083000Z
DTSTAMP;VALUE=DATE-TIME:20220816T031724Z
UID:OISTRTS/33
DESCRIPTION:Title: An example of A2 Rogers-Ramanujan bipartition identities of level 3\n
by Shinsuke Tsuchioka (Tokyo Institute of Technology) as part of OIST repr
esentation theory seminar\n\n\nAbstract\nIn the 1970s\, Lepowsky-Milne dis
covered a similarity between the infinite products of the Rogers-Ramanujan
identities (RR identities\, for short) and the principal characters of th
e level 3 standard modules of the affine Lie algebra of type \\(A^{(1)}_{1
}\\). Subsequently\, Lepowsky-Wilson gave a Lie-theoretic interpretation a
nd a proof of the RR identities with the vertex operators. In this talk\,
I will present some results (arXiv:2205.04811) for the level 3 case of typ
e \\(A^{(1)}_{2}\\).\n
LOCATION:https://researchseminars.org/talk/OISTRTS/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rob Muth (Duquesne University)
DTSTART;VALUE=DATE-TIME:20220705T073000Z
DTEND;VALUE=DATE-TIME:20220705T083000Z
DTSTAMP;VALUE=DATE-TIME:20220816T031724Z
UID:OISTRTS/34
DESCRIPTION:Title: Superalgebra deformations of web categories\nby Rob Muth (Duquesne Un
iversity) as part of OIST representation theory seminar\n\n\nAbstract\nFor
a superalgebra A\, and even subalgebra a\, one may define an associated d
iagrammatic monoidal supercategory Web(A\,a)\, which generalizes a number
of symmetric web category constructions. In this talk\, I will define and
discuss Web(A\,a)\, focusing on two interesting applications: Firstly\, We
b(A\,a) is equipped with an asymptotically faithful functor to the categor
y of gl_n(A)-modules generated by symmetric powers of the natural module\,
and may be used to establish Howe dualities between gl_n(A) and gl_m(A) i
n some cases. Secondly\, Web(A\,a) yields a diagrammatic presentation for
the ‘Schurification' T^A_a(n\,d). For various choices of A/a\, these Sch
urifications have proven connections to RoCK blocks of Hecke algebras\, an
d conjectural connections to RoCK blocks of Schur algebras and Sergeev sup
eralgebras. This is joint work with Nicholas Davidson\, Jonathan Kujawa\,
and Jieru Zhu.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Mathas (University of Sydney)
DTSTART;VALUE=DATE-TIME:20220810T060000Z
DTEND;VALUE=DATE-TIME:20220810T070000Z
DTSTAMP;VALUE=DATE-TIME:20220816T031724Z
UID:OISTRTS/35
DESCRIPTION:Title: Content systems and KLR algebras\nby Andrew Mathas (University of Syd
ney) as part of OIST representation theory seminar\n\n\nAbstract\nIn 1901
Young gave an explicit construction of the ordinary irreducible representa
tions of the symmetric groups. In doing this\, he introduced content funct
ions for partitions\, which are now a key statistic in the semisimple repr
esentation theory of the symmetric groups. In this talk I will describe a
generalisation of Young's ideas to the cyclotomic KLR algebras of affine t
ypes A and C. This is quite surprising because Young's seminormal forms ar
e creatures from the semisimple world whereas the cyclotomic KLR algebras
are rarely semisimple. As an application\, we show that these algebras are
cellular and construct their irreducible representations. A special case
of these results gives new information about the symmetric groups in chara
cteristic p>0. If time permits\, I will describe how these results lead to
an explicit categorification of the corresponding integrable highest weig
ht modules.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alice Dell'Arciprete (University of East Anglia)
DTSTART;VALUE=DATE-TIME:20220719T073000Z
DTEND;VALUE=DATE-TIME:20220719T083000Z
DTSTAMP;VALUE=DATE-TIME:20220816T031724Z
UID:OISTRTS/36
DESCRIPTION:Title: Scopes equivalence for blocks of Ariki-Koike algebras\nby Alice Dell'
Arciprete (University of East Anglia) as part of OIST representation theor
y seminar\n\n\nAbstract\nWe consider representations of the Ariki-Koike al
gebra\, a $q$-deformation of the group algebra of the complex reflection g
roup $C_r \\wr S_n$. The representations of this algebra are naturally ind
exed by multipartitions of $n$. We examine blocks of the Ariki-Koike algeb
ra\, in an attempt to generalise the combinatorial representation theory o
f the Iwahori-Hecke algebra. In particular\, we prove a sufficient conditi
on such that restriction of modules leads to a natural correspondence betw
een the multipartitions of $n$ whose Specht modules belong to a block $B$
and those of $n-\\delta_i(B)$ whose Specht modules belong to the block $B'
$\, obtained from $B$ applying a Scopes' equivalence.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sinéad Lyle (University of East Anglia)
DTSTART;VALUE=DATE-TIME:20220721T073000Z
DTEND;VALUE=DATE-TIME:20220721T083000Z
DTSTAMP;VALUE=DATE-TIME:20220816T031724Z
UID:OISTRTS/37
DESCRIPTION:Title: Rouquier blocks for Ariki-Koike algebras\nby Sinéad Lyle (University
of East Anglia) as part of OIST representation theory seminar\n\n\nAbstra
ct\nThe Rouquier blocks\, also known as the RoCK blocks\, are important bl
ocks of the symmetric groups algebras and the Hecke algebras of type $A$\,
with the partitions labelling the Specht modules that belong to these blo
cks having a particular abacus configuration. We generalise the definition
of Rouquier blocks to the Ariki-Koike algebras\, where the Specht modules
are indexed by multipartitions\, and explore the properties of these bloc
ks.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/37/
END:VEVENT
END:VCALENDAR