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BEGIN:VEVENT
SUMMARY:Bojko Bakalov (North Carolina State University)
DTSTART:20200908T170000Z
DTEND:20200908T180000Z
DTSTAMP:20260422T225637Z
UID:RepTheoryMathPhys/1
DESCRIPTION:Title: A vertex algebra construction of representations of toroidal Lie
algebras\nby Bojko Bakalov (North Carolina State University) as part
of Representation Theory and Mathematical Physics Seminar\n\n\nAbstract\nG
iven a simple finite-dimensional Lie algebra and an automorphism of\nfinit
e order\, one can construct a twisted toroidal Lie algebra.\nSimilarly to
twisted affine Lie algebras\, which are well-studied in\nthe literature\,
we can create representations of twisted toroidal Lie\nalgebras with the h
elp of vertex algebras. In this talk\, I will\ndiscuss twisted modules of
vertex algebras and will show how\nrepresentations of twisted toroidal Lie
algebras can be constructed\nfrom such twisted modules. Joint work with S
amantha Kirk.\n
LOCATION:https://researchseminars.org/talk/RepTheoryMathPhys/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Misha Feigin (University of Glasgow)
DTSTART:20200915T170000Z
DTEND:20200915T180000Z
DTSTAMP:20260422T225637Z
UID:RepTheoryMathPhys/2
DESCRIPTION:Title: Lassalle-Nekrasov correspondence for Calogero-Moser systems and
quasi-invariant Hermite polynomials\nby Misha Feigin (University of Gl
asgow) as part of Representation Theory and Mathematical Physics Seminar\n
\n\nAbstract\nLassalle and Nekrasov observed in the 1990s relations betwee
n the rational Calogero-Moser system with harmonic term and the trigonomet
ric Calogero-Moser system. In the quantum case this amounts to an operator
on the algebra of symmetric polynomials which intertwines actions of corr
esponding quantum integrals of these two systems. I would like to explain
this relation and its generalisations by making use of automorphisms of th
e rational Cherednik algebra. For integer coupling parameter the algebra o
f symmetric polynomials can be extended by quasi-invariants\, which is a m
odule for the spherical subalgebra of Cherednik algebra\, and we get a cla
ss of non-symmetric polynomials which are eigenfunctions of the rational H
amiltonian. The talk is based on joint work with Martin Hallnäs and Alexa
nder Veselov.\n
LOCATION:https://researchseminars.org/talk/RepTheoryMathPhys/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Saber Ahmed (University of Texas at Arlington)
DTSTART:20200922T170000Z
DTEND:20200922T180000Z
DTSTAMP:20260422T225637Z
UID:RepTheoryMathPhys/3
DESCRIPTION:Title: Quantized enveloping superalgebra of type $P$\nby Saber Ahme
d (University of Texas at Arlington) as part of Representation Theory and
Mathematical Physics Seminar\n\n\nAbstract\nWe introduce a new quantized e
nveloping superalgebra $U_q({\\mathfrak p}(n))$ that is a quantization of
the Lie bisuperalgebra structure on the periplectic Lie superalgebra ${\\m
athfrak p}(n)$. We show some of the basic properties of the quantization.
We also introduce the periplectic $q$-Brauer algebra. This is a joint work
with D. Grantcharov and N. Guay.\n
LOCATION:https://researchseminars.org/talk/RepTheoryMathPhys/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Siddhartha Sahi (Rutgers University)
DTSTART:20200929T170000Z
DTEND:20200929T180000Z
DTSTAMP:20260422T225637Z
UID:RepTheoryMathPhys/4
DESCRIPTION:Title: Lie superalgebras and the Capelli eigenvalue problem\nby Sid
dhartha Sahi (Rutgers University) as part of Representation Theory and Mat
hematical Physics Seminar\n\n\nAbstract\nThe classical Capelli operator of
19th century invariant theory is a differential operator on $n \\times n$
matrices\, which is closely related to the determinant. In the 1980s\, Be
rtram Kostant and the speaker found a natural generalization of this to a
Jordan algebra $J$\, with the determinant replaced by the Jordan norm poly
nomial.The differential operators that arise in this manner belong to the
algebra $D(X)$ of invariant differential operators on a certain symmetric
space $X$ associated to $J$.\n\n In the 1990s\, the speaker extended th
ese ideas to obtain a *basis* of $D(X)$\, now called the "Capelli basis"\,
and computed their eigenvalues. By a general result of Harish-Chandra\, t
he eigenvalues of an invariant differential operator $T$ are special value
s of an associated Weyl group invariant polynomial $p_T$. For the Capelli
basis\, the polynomials $p_T$ are special cases of a remarkable family of
polynomials defined by certain elementary vanishing conditions\, or interp
olation properties.\n\n Subsequently\, Friedrich Knop and the speaker di
scovered an unexpected connection between the more general "interpolation
polynomials" and Jack polynomials. This led to new insights into Jack poly
nomials\, and subsequently for Macdonald polynomials and double affine Hec
ke algebras\, resulting in the proofs of certain conjectures by Macdonald.
\n\n In this talk I will describe the extension of some of these ideas
to Jordan superalgebras and symmetric superspaces obtained in recent work
by Vera Serganova\, Hadi Salmasian\, and the speaker\, building on earlier
joint work with Salmasian and Alexander Alldridge. This offers some new i
nsights into the representation theory of Lie superalgebras. It also opens
a new perspective on interpolation polynomials themselves\, revealing a c
onnection with Deligne's interpolation categories. It has also revealed a
remarkable new connection with something almost as old as the original Cap
elli operator\, namely the Dougall-Ramanujan identity\, dubbed by Ekhad an
d Zeilberger as "one of the most beautiful and general results in the theo
ry of hypergeometric series".\n
LOCATION:https://researchseminars.org/talk/RepTheoryMathPhys/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vyacheslav Futorny (Universidade de Sao Paulo)
DTSTART:20201006T170000Z
DTEND:20201006T180000Z
DTSTAMP:20260422T225637Z
UID:RepTheoryMathPhys/5
DESCRIPTION:Title: Positive energy representations of affine vertex algebras via lo
calization\nby Vyacheslav Futorny (Universidade de Sao Paulo) as part
of Representation Theory and Mathematical Physics Seminar\n\n\nAbstract\nT
his is a joint work with Libor Krizka. We introduce a Wakimoto functor fro
m a certain category of modules over a simple finite-dimensional Lie algeb
ra to the category of positive energy modules over the corresponding affin
e Kac-Moody algebra. Combining the Wakimoto functor with the localization
functor we construct new families of positive energy representations of a
ffine vertex algebras together with their free field realizations.\n
LOCATION:https://researchseminars.org/talk/RepTheoryMathPhys/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sophie Morier-Genoud (Sorbonne Université\, Paris)
DTSTART:20201013T170000Z
DTEND:20201013T180000Z
DTSTAMP:20260422T225637Z
UID:RepTheoryMathPhys/6
DESCRIPTION:Title: $q$-analogues of rational and real numbers\nby Sophie Morier
-Genoud (Sorbonne Université\, Paris) as part of Representation Theory an
d Mathematical Physics Seminar\n\n\nAbstract\nClassical sequences of numbe
rs often lead to interesting $q$-analogues. The most popular among them ar
e certainly the $q$-integers and the $q$-binomial coefficients which both
appear in various areas of mathematics and physics. It seems that q-analog
ues of rational numbers have been much less popular so far. We suggest a d
efinition based on combinatorial properties of the rational numbers and co
ntinued fractions. The definition of $q$-rationals naturally extends the o
ne of $q$-integers and leads to a ratio of polynomials with positive integ
er coefficients. One can give enumerative interpretations of the coefficie
nts in terms of graphs or quiver representations. There are also links to
the Jones polynomials and to cluster algebras. Finally the definition of q
-rationals extends to a definition for $q$-real numbers. This is joint wor
k with Valentin Ovsienko.\n
LOCATION:https://researchseminars.org/talk/RepTheoryMathPhys/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vera Serganova (University of California\, Berkeley)
DTSTART:20201020T170000Z
DTEND:20201020T180000Z
DTSTAMP:20260422T225637Z
UID:RepTheoryMathPhys/7
DESCRIPTION:Title: Tensor product of the Fock representation with its dual.\nby
Vera Serganova (University of California\, Berkeley) as part of Represen
tation Theory and Mathematical Physics Seminar\n\n\nAbstract\nLet $F$ deno
te the Fock representation for $sl(\\infty)$. We describe the structure of
the tensor product of $F$ with its restricted dual $F^*$. In particular w
e prove that this module has a decreasing filtration with simple quotients
and show that such filtration is unique. The proof uses categorification
of the abelian envelope of Deligne category $GL(t)$ for integer $t$ and th
e category of finite-dimensional representations of the supergroup $GL(m|n
)$ with $m-n=t$.\n
LOCATION:https://researchseminars.org/talk/RepTheoryMathPhys/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Gorelik (Weizmann Institute of Science)
DTSTART:20201027T170000Z
DTEND:20201027T180000Z
DTSTAMP:20260422T225637Z
UID:RepTheoryMathPhys/8
DESCRIPTION:Title: Arc diagrams and Duflo-Serganova functor $DS_x$\nby Maria Go
relik (Weizmann Institute of Science) as part of Representation Theory and
Mathematical Physics Seminar\n\n\nAbstract\nLet $L$ be a simple finite-d
imensional module over a Lie superalgebra $\\mathfrak g$. We would like t
o describe the $DS_x({\\mathfrak g})$-module $DS_x(L)$. For the algebras
$\\mathfrak{gl}(m|n)$\, $\\mathfrak{osp}(m|n)$ and $\\mathfrak{p}(n)$\, th
e answer can be nicely expressed in terms of a combinatorial gadget\, the
arc diagram\, assigned to $L$. In this talk I will review the constructio
ns of arc diagrams. The talk is based on the results of Heidersdorf - Weis
sauer\, Entova-Aizenbud - Serganova and Gorelik - Heidersdorf.\n
LOCATION:https://researchseminars.org/talk/RepTheoryMathPhys/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johan van de Leur (Utrecht University)
DTSTART:20201103T180000Z
DTEND:20201103T190000Z
DTSTAMP:20260422T225637Z
UID:RepTheoryMathPhys/9
DESCRIPTION:Title: The Extended Toda and Non-Linear Schroedinger Hierarchies\nb
y Johan van de Leur (Utrecht University) as part of Representation Theory
and Mathematical Physics Seminar\n\n\nAbstract\nWe study the integrable sy
stem which is related a Dubrovin–Frobenius manifold of rank $2$ whose ge
nus expansion $D$ at a special point controls enumeration of a higher gene
ra generalization of the Catalan numbers. In particular\, we will give a H
irota bilinear equation for this $D$ and show that this leads to a Lax for
mulation of both the Carlet-Dubrovin-Zhang Extended Toda Hierarch and to t
he extended Non-Linear Schroedinger hierarchy. This is based on joint work
with Guido Carlet\, Hessel Posthuma and Sergey Shadrin.\n
LOCATION:https://researchseminars.org/talk/RepTheoryMathPhys/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Letterio Gatto (Politecnico di Torino)
DTSTART:20201110T180000Z
DTEND:20201110T190000Z
DTSTAMP:20260422T225637Z
UID:RepTheoryMathPhys/10
DESCRIPTION:Title: Bosonic and Fermionic Representations of Endomorphisms of Exter
ior Algebras\nby Letterio Gatto (Politecnico di Torino) as part of Rep
resentation Theory and Mathematical Physics Seminar\n\n\nAbstract\nThe abs
tract is available at:\nhttps://www.math.ksu.edu/research/files_mathphysre
p_seminar/KSU_RTMPS_Gatto.pdf\n
LOCATION:https://researchseminars.org/talk/RepTheoryMathPhys/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Mnev (University of Notre Dame)
DTSTART:20201117T180000Z
DTEND:20201117T190000Z
DTSTAMP:20260422T225637Z
UID:RepTheoryMathPhys/11
DESCRIPTION:Title: Two-dimensional BF theory as a conformal field theory\nby P
avel Mnev (University of Notre Dame) as part of Representation Theory and
Mathematical Physics Seminar\n\n\nAbstract\nWe study topological BF theory
on the complex plane in Lorenz gauge. In the abelian case\, we find that
the gauge-fixed theory is a B-twisted $N=(2\,2)$ superconformal theory - W
itten's B-model with a parity-reversed target. The BV algebra structure on
0-observables is constructed explicitly using operator product expansions
with the superpartner of the stress-energy tensor. In the non-abelian ca
se\, the theory becomes a logarithmic CFT with correlators given by conver
gent integrals (e.g.\, 4-point functions are expressed in terms of dilogar
ithms). We find vertex operators in the non-abelian theory\, receiving a q
uantum correction to conformal dimension. This is a report on a joint work
with Andrey Losev and Donald Youmans\, arXiv:1712.01186\, arXiv:1902.0273
8\n
LOCATION:https://researchseminars.org/talk/RepTheoryMathPhys/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Petrov (University of Virginia)
DTSTART:20201201T180000Z
DTEND:20201201T190000Z
DTSTAMP:20260422T225637Z
UID:RepTheoryMathPhys/12
DESCRIPTION:Title: Symmetric functions from integrable vertex models\nby Leoni
d Petrov (University of Virginia) as part of Representation Theory and Mat
hematical Physics Seminar\n\n\nAbstract\nI will discuss how properties of
symmetric functions (such as Schur and Hall-Littlewood functions and their
generalizations) arise from studying integrable vertex models. The focus
will be on (1) summation identities\; (2) a new class of continuously-inde
xed spin Whittaker symmetric functions generalizing the 2F1 hypergeometric
functions and the gl_n Whittaker functions. The second part is based on a
joint work with Matteo Mucciconi.\n
LOCATION:https://researchseminars.org/talk/RepTheoryMathPhys/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonas Hartwig (Iowa State University)
DTSTART:20210126T180000Z
DTEND:20210126T190000Z
DTSTAMP:20260422T225637Z
UID:RepTheoryMathPhys/13
DESCRIPTION:Title: Harish-Chandra modules over orders in smash products\nby Jo
nas Hartwig (Iowa State University) as part of Representation Theory and M
athematical Physics Seminar\n\n\nAbstract\nFor an integral domain $\\Lambd
a$ with fraction field $L$\, we study a class of noncommutative $\\Lambda$
-orders $F$ in a smash product of $L$ by a Hopf algebra. Specifically we g
ive a sufficient condition for there to be only finitely many isoclasses o
f simple $F$-modules that are locally finite for $\\Lambda$ and are suppor
ted on a given maximal ideal of $\\Lambda$. This generalizes a "finiteness
of fibers" theorem of Futorny and Ovsienko for Galois orders. We point ou
t some connections to Gelfand-Tsetlin theory for $\\mathfrak{gl}_n$\, Hopf
Galois extensions and Cherednik algebras.\n
LOCATION:https://researchseminars.org/talk/RepTheoryMathPhys/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Volodymyr Mazorchuk (Uppsala University)
DTSTART:20210202T180000Z
DTEND:20210202T190000Z
DTSTAMP:20260422T225637Z
UID:RepTheoryMathPhys/14
DESCRIPTION:Title: Images of simple modules under projective functors and Kostant'
s problem\nby Volodymyr Mazorchuk (Uppsala University) as part of Repr
esentation Theory and Mathematical Physics Seminar\n\n\nAbstract\nIn this
talk I will try to report on recent progress in connection to the classica
l Kostant's problem which asks when the unviersal enveloping algebra surje
cts onto the space of adjointly finite endomorphisms of a simple highest w
eight module. In particular\, I will describe how this is connect to the p
roblem of indecomposability of images of simple highest weight modules und
er indecomposable projective\nfunctors.\n This is a joint work with Hankyu
ng Ko and Rafael Mrden.\n
LOCATION:https://researchseminars.org/talk/RepTheoryMathPhys/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alistair Savage (University of Ottawa)
DTSTART:20210209T180000Z
DTEND:20210209T190000Z
DTSTAMP:20260422T225637Z
UID:RepTheoryMathPhys/15
DESCRIPTION:Title: Affinization of monoidal categories\nby Alistair Savage (Un
iversity of Ottawa) as part of Representation Theory and Mathematical Phys
ics Seminar\n\n\nAbstract\nWe define the affinization of an arbitrary mono
idal category\, corresponding to the category of string diagrams on the cy
linder. We also give an alternative characterization in terms of adjoinin
g dot generators to the category. The affinization formalizes and unifies
many constructions appearing in the literature. We describe a large numb
er of examples coming from Hecke-type algebras\, braids\, tangles\, and kn
ot invariants.\n
LOCATION:https://researchseminars.org/talk/RepTheoryMathPhys/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg Sheinman (Steklov Mathematical Institute\, Moscow)
DTSTART:20210216T180000Z
DTEND:20210216T190000Z
DTSTAMP:20260422T225637Z
UID:RepTheoryMathPhys/16
DESCRIPTION:Title: Lax representation and separation of variables for Hitchin syst
ems\nby Oleg Sheinman (Steklov Mathematical Institute\, Moscow) as pa
rt of Representation Theory and Mathematical Physics Seminar\n\n\nAbstract
\nThe Hitchin systems were invented in 1987 and since that time have been\
nsuccessfully applied in geometric Langlands program\, Supersymmetric\nMo
dels of quantum field theory (SUSY)\, 2D CFT and in other fields. In\n198
7-97 Hitchin systems have been investigated mainly by methods of\nalgebrai
c geometry but later it was realized that they also need to be\ninvestigat
ed by specific methods of the theory of integrable systems\n(K.Gawedzki’
98\, R.Donagi\, E.Witten’95\, A.Gorsky\, N.Nekrasov\,\nV.Rubtsov’01\,
I.Krichever’01). In my talk\, I will report on some\nexplicit results in
this direction. To begin with\, I shall define\nHitchin systems by means
of the Lax representation with spectral\nparameter on a Riemann surface. F
or Lax operators taking values in gl(n)\nit is due to I.Krichever (2001).
Based on the description of gradings of\ncomplex semi-simple Lie algebras\
, I shall give the definition in the\ncase of an arbitrary Lie algebra of
that class (mainly focusing on the\nsimple case). Then I’ll describe th
e universal spectral curve for\nHitchin systems on hyperelliptic curves. I
t makes possible to apply the\nclassical method of separation of variables
. Following this line\, I’ll\ngive completely explicit (at least for Lie
algebras An\, Bn\, Cn\, and\nhyperelliptic curves) expressions for the Ha
miltonians and angle\nvariables of Hitchin systems.\n\n
References\nO. K. Sheinman. Lax operator algebras and integrable systems.
Russian\nMath. Surveys\, 71:1 (2016)\, 109–156\; arXiv:1602.04320.\n\nO.
K.Sheinman. Spectral curves of the hyperelliptic Hitchin systems.\nFunct.
Anal. Appl.\, 53:4 (2019)\, 291–303\; arXiv:1806.10178.\n\nP.I.Borisova\
, O.K.Sheinman. Hitchin systems on hyperelliptic curves.\nProceedings of t
he Steklov Mathematical Institute\, Vol. 311\, 2020\;\narXiv:1912.06849.\n
LOCATION:https://researchseminars.org/talk/RepTheoryMathPhys/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Harnad (Concordia University\, Mathematical Physics Lab\, Cen
tre de recherches mathématiques)
DTSTART:20210223T180000Z
DTEND:20210223T190000Z
DTSTAMP:20260422T225637Z
UID:RepTheoryMathPhys/17
DESCRIPTION:Title: Bilinear expansions of lattices of KP $\\tau$-function in BKP
$\\tau$-functions: a fermionic approach\nby John Harnad (Concordia Uni
versity\, Mathematical Physics Lab\, Centre de recherches mathématiques)
as part of Representation Theory and Mathematical Physics Seminar\n\n\nAbs
tract\nThe notion of Kadomtsev-Petviashvili (KP) and BKP $\\tau$ functions
will\nbe recalled\, together with their representations as fermionic expe
ctation values.\nSchur-type lattices of such KP and BKP $\\tau$-functions
will be defined\, corresponding to\na given infinite general linear or ort
hogonal group element\, labelled by partitions\nand strict partitions resp
ectively. A bilinear expansion expressing elements of these lattices of KP
$\\tau$-functions as sums over products of pairs of elements of associate
d lattices of BKP $\\tau$-functions will be presented\, generalizing earl
ier results relating determinants and Pfaffians of minors of skew symmetr
ic matrices\, with applications to Schur functions and Schur $Q$-functions
. Further applications include inhomogeneous polynomial $\\tau$-functions
of KP and BKP type\, with their determinantal and Pfaffian representations
.\n
LOCATION:https://researchseminars.org/talk/RepTheoryMathPhys/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vidas Regelskis (University of Hertfordshire)
DTSTART:20210302T180000Z
DTEND:20210302T190000Z
DTSTAMP:20260422T225637Z
UID:RepTheoryMathPhys/18
DESCRIPTION:Title: R-matrix presentation of orthogonal and symplectic quantum loop
algebras\nby Vidas Regelskis (University of Hertfordshire) as part of
Representation Theory and Mathematical Physics Seminar\n\n\nAbstract\nIn
this talk I will present an R-matrix approach to quantum loop\nalgebras as
sociated with the simple Lie algebras of orthogonal and\nsymplectic types.
One of the main advantages of the R-matrix approach\nover the Drinfeld ne
w presentation is that both untwisted and twisted\ncases can be considered
seamlessly with no extra effort. I will also\ndiscuss challenges and adva
ntages of the R-matrix approach in proving\nthe PBW theorem and constructi
ng highest-weight representations\, and\nrediscovering the classical resul
ts of Chari and Pressley.\n
LOCATION:https://researchseminars.org/talk/RepTheoryMathPhys/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julia Pevtsova (University of Washington)
DTSTART:20210420T170000Z
DTEND:20210420T180000Z
DTSTAMP:20260422T225637Z
UID:RepTheoryMathPhys/19
DESCRIPTION:Title: Support and tensor product property for integrable finite dimen
sional Hopf algebras.\nby Julia Pevtsova (University of Washington) as
part of Representation Theory and Mathematical Physics Seminar\n\n\nAbstr
act\nFor a finite dimensional Hopf algebra A the cohomological support on
the stable category Stab A can be defined via the Benson-Iyengar-Krause th
eory of local cohomology functors\, with no reference to the tensor struct
ure.\n\n Yet\, for various finite tensor categories the cohomological sup
port turns out to respect that structure via the “tensor product propert
y”: $supp(M \\otimes N) = supp M \\cap supp N$. \nWhen the property hold
s\, it often appears to be intimately connected with some kind of alternat
ive description of the cohomological support\, “a rank variety”. I’l
l describe such an alternative construction\, the hypersurface support\, w
hich goes back to the work of Eisenbud\, Avramov\, Buchweitz and Iyengar i
n commutative algebra\, in the case of a finite dimensional integrable Hop
f algebra. Applications include (only some) small quantum groups\, quantum
linear spaces\, Drinfeld doubles of finite group schemes\, rings of funct
ions on finite group schemes and elementary finite supergroup schemes. Joi
nt work with C. Negron and D. Benson\, S. Iyengar\, H. Krause.\n
LOCATION:https://researchseminars.org/talk/RepTheoryMathPhys/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Evgeny Mukhin (IUPUI)
DTSTART:20210316T170000Z
DTEND:20210316T180000Z
DTSTAMP:20260422T225637Z
UID:RepTheoryMathPhys/20
DESCRIPTION:Title: Characters\, q-characters\, and qq-characters\nby Evgeny Mu
khin (IUPUI) as part of Representation Theory and Mathematical Physics Sem
inar\n\n\nAbstract\nThe q-characters of finite dimensional modules of affi
ne quantum groups describe the cancellation of poles of transfer matrices
in analytic Bethe ansatz. The qq-characters are combinatorial objects whi
ch describe the commutation of deformed W-currents with screening charges
in a similar way.\n\nIn this talk I will try to give an elementary introdu
ction to the theory of q- and qq-characters\, discuss the related combinat
orics and outline the main ideas and challenges in the area.\n
LOCATION:https://researchseminars.org/talk/RepTheoryMathPhys/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oksana Yakimova (Friedrich-Schiller-Universität Jena Mathematisch
es Institut)
DTSTART:20210323T170000Z
DTEND:20210323T180000Z
DTSTAMP:20260422T225637Z
UID:RepTheoryMathPhys/21
DESCRIPTION:Title: On the Feigin-Frenkel centre and its applications to quantisati
on problems\nby Oksana Yakimova (Friedrich-Schiller-Universität Jena
Mathematisches Institut) as part of Representation Theory and Mathematical
Physics Seminar\n\n\nAbstract\nLet $G$ be a complex reductive group\, set
$\\mathfrak g={\\mathrm{Lie\\\,}}G$. The symmetric algebra ${\\mathcal S
}(\\mathfrak g)$ is equipped with the standard Lie—Poisson bracket and a
subalgebra $A\\subset {\\mathcal S}(\\mathfrak g)$ is Poisson-commutative
if this bracket vanishes on $A$. Since ${\\mathcal S}(\\mathfrak g)$ is t
he associated graded of the enveloping algebra ${\\mathcal U}(\\mathfrak g
)$\, it is natural to ask\, whether a given Poisson-commutative $A\\subset
{\\mathcal S}(\\mathfrak g)$ has a quantisation (a lift to a commutative
subalgebra of ${\\mathcal U}(\\mathfrak g)$).\n
LOCATION:https://researchseminars.org/talk/RepTheoryMathPhys/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hadi Salmasian (University of Ottawa)
DTSTART:20210330T170000Z
DTEND:20210330T180000Z
DTSTAMP:20260422T225637Z
UID:RepTheoryMathPhys/22
DESCRIPTION:Title: Capelli problems for basic classical Lie superalgebras\nby
Hadi Salmasian (University of Ottawa) as part of Representation Theory and
Mathematical Physics Seminar\n\n\nAbstract\nLet $g$ be a basic classical
Lie superalgebra and let $V$ be a representation of $g$ such that $S(V)$ i
s a multiplicity-free $g$-module. In this setting\, one can construct a na
tural basis for the algebra of $g$-invariant (super)polynomial differentia
l operators on $V$. When the pair $(g\,V)$ arises from the Tits-Kantor-Koe
cher construction\, we compute an explicit formula for the eigenvalues of
this family of operators. We connect this formula to the deformed root sys
tems of type $A(m\,n)$ that were studied by Sergeev and Veselov. As a bypr
oduct\, we prove that for $(g\,V)$ associated to the exceptional 10-dimens
ional Jordan superalgebra\, the abstract Capelli problem (in the sense of
Howe and Umeda) has a negative answer. Based on joint work with S. Sahi an
d V. Serganova.\n
LOCATION:https://researchseminars.org/talk/RepTheoryMathPhys/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Irina Kashuba (Institute of Mathematics and Statistics University
of Sao Paulo)
DTSTART:20210427T170000Z
DTEND:20210427T180000Z
DTSTAMP:20260422T225637Z
UID:RepTheoryMathPhys/23
DESCRIPTION:Title: Representation type of Jordan algebras and superalgebras\nb
y Irina Kashuba (Institute of Mathematics and Statistics University of Sao
Paulo) as part of Representation Theory and Mathematical Physics Seminar\
n\n\nAbstract\nWe will review recent and classical results on the represen
tations of finite dimensional Jordan algebras and superalgebras. We will w
eigh the pros against the cons of using the Tits-Kantor-Koecher constructi
on for this problem.\n\nThe seminar presentation is joint with Springfe
st in honor of Vera Serganova\nhttps://innaentova.wixsite.com/springfest20
21\n
LOCATION:https://researchseminars.org/talk/RepTheoryMathPhys/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zongzhu Lin (Kansas State University)
DTSTART:20210406T170000Z
DTEND:20210406T180000Z
DTSTAMP:20260422T225637Z
UID:RepTheoryMathPhys/24
DESCRIPTION:Title: Irreducible characters for algebraic groups in positive charact
eristics and quantum groups at $p^r$-th roots of 1.\nby Zongzhu Lin (K
ansas State University) as part of Representation Theory and Mathematical
Physics Seminar\n\n\nAbstract\nIrreducible characters for reductive algebr
aic groups in positive characteristic $p$ cases were conjectured by Luszti
g in terms of Weyl characters using Kazhdan-Lusztig polynomials when the h
ighest weight is reasonably within the $p^2$-alcove. When $p$ is sufficien
tly large such that all restricted dominant weights are within this region
\, Lusztig conjectured formula would give all irreducible characters using
the Steinberg tensor product theorem. However decomposing Weyl character
s in terms of irreducible characters and expressing irreducible characters
in terms of Weyl characters becomes much more complicated when the highes
t weight is outside of $p^2$ alcove. In 2014\, Lusztig gave a recursive fo
rmula to computing these dcomposition numbers. In this talk\, I will use t
he irreducible characters for quantum groups at $p^r$-th roots of unity as
middle bridge for $r=1\, 2\, …$ to express the decomposition numbers in
terms of Kazhdan Lusztig polynomials with different affine Weyl group act
ions on the weight lattice through Frobenius twists. When r=1\, we recover
Lusztig’s formula. Not only we get infinite family of Z-bases for the W
eyl group invariants in the group ring of the weight lattices\, but we als
o obtain infinite families of highest weight modules corresponding to thes
e bases.\n
LOCATION:https://researchseminars.org/talk/RepTheoryMathPhys/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thorsten Heidersdorf (Mathematical Institute of the University of
Bonn)
DTSTART:20210413T170000Z
DTEND:20210413T180000Z
DTSTAMP:20260422T225637Z
UID:RepTheoryMathPhys/25
DESCRIPTION:Title: Monoidal structures for supergroups\nby Thorsten Heidersdor
f (Mathematical Institute of the University of Bonn) as part of Representa
tion Theory and Mathematical Physics Seminar\n\n\nAbstract\nVery little is
known about the rules governing the tensor product decomposition between
irreducible representations of an algebraic supergroup. It turns out that
one can understand the decomposition "up to superdimension 0". For $GL(m|n
)$ ($m \\geq n$) this can in some way be reduced to the case $GL(m|2)$\, s
o I will mostly discuss this case along with some preliminary results for
$OSp(m|2n)$.\n
LOCATION:https://researchseminars.org/talk/RepTheoryMathPhys/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Khoa Nguyen (University of Texas\, Arlington)
DTSTART:20210309T180000Z
DTEND:20210309T190000Z
DTSTAMP:20260422T225637Z
UID:RepTheoryMathPhys/26
DESCRIPTION:Title: Exponentiation functors on differential operators of $\\mathfra
k{sl}(n+1)$.\nby Khoa Nguyen (University of Texas\, Arlington) as part
of Representation Theory and Mathematical Physics Seminar\n\n\nAbstract\n
With the aid of the exponentiation functor and Fourier transform we introd
uce modules $T (g\, V\, S)$ of differential operators of $\\mathfrak{sl}
(n + 1)$. Here $g$ is a polynomial of n variables\, $V$ is a $\\mathfrak{g
l}(n)$-module\, and $S$ is a subset of $\\{1\,2\,…\,n\\}$. By varying $g
\,V\,S$ we obtain various families of modules of $\\mathfrak{sl}(n + 1)$.
Some of these families contain weight modules (i.e. with a semisimle actio
n of the Cartan subalgebra $\\mathfrak h$)\, while others contain $\\mathf
rak h$-free modules. An isomorphism theorem and simplicity criterion for $
T (g\, V\, S)$ will be provided. This is based on a joint work with D. Gra
ntcharov.\n
LOCATION:https://researchseminars.org/talk/RepTheoryMathPhys/26/
END:VEVENT
END:VCALENDAR