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SUMMARY:Toshiyuki Kobayashi (The University of Tokyo)
DTSTART;VALUE=DATE-TIME:20210908T070000Z
DTEND;VALUE=DATE-TIME:20210908T075000Z
DTSTAMP;VALUE=DATE-TIME:20220528T192235Z
UID:AIM-RTNCG-SemRepTh/1
DESCRIPTION:Title: Tempered representations and limit algebras\nby Toshiyuki K
obayashi (The University of Tokyo) as part of Seminar in Representation Th
eory\n\n\nAbstract\nI plan to discuss some new connection between the foll
owing four (apparently un-\nrelated) topics:\n\n(1) (analysis) Tempered un
itary representations on homogeneous spaces\n\n(2) (combinatorics) Convex
polyhedral cones\n\n(3) (topology) Limit algebras\n\n(4) (symplectic geome
try) Quantization of coadjoint orbits\,\n\nbased on a series of joint pape
rs with Y. Benoist "Tempered homogeneous spaces\nI–IV".\n
LOCATION:https://researchseminars.org/talk/AIM-RTNCG-SemRepTh/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chen-Bo Zhu (National University of Singapore)
DTSTART;VALUE=DATE-TIME:20210908T075000Z
DTEND;VALUE=DATE-TIME:20210908T084000Z
DTSTAMP;VALUE=DATE-TIME:20220528T192235Z
UID:AIM-RTNCG-SemRepTh/2
DESCRIPTION:Title: Theta correspondence and special unipotent representations\
nby Chen-Bo Zhu (National University of Singapore) as part of Seminar in R
epresentation Theory\n\n\nAbstract\nThe theory of theta correspondence\, i
nitiated by Howe\, provides a powerful method of constructing irreducible
admissible representations of classical Lie groups. In this talk\, I will
discuss a recent work\, joint with Barbasch\, Ma and Sun\, in which we sho
w that in addition to irreducible unitary parabolic inductions\, theta lif
ts yield all special unipotent representations of a classical Lie group $G
$. As a consequence of the construction and the classification\, we conclu
de that all special unipotent representations of $G$ are unitarizable\, as
predicted by the Arthur--Barbasch--Vogan conjecture.\n
LOCATION:https://researchseminars.org/talk/AIM-RTNCG-SemRepTh/2/
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SUMMARY:Wee Teck Gan (National University of Singapore)
DTSTART;VALUE=DATE-TIME:20210908T090000Z
DTEND;VALUE=DATE-TIME:20210908T095000Z
DTSTAMP;VALUE=DATE-TIME:20220528T192235Z
UID:AIM-RTNCG-SemRepTh/3
DESCRIPTION:Title: Twisted GGP problems and conjectures\nby Wee Teck Gan (Nati
onal University of Singapore) as part of Seminar in Representation Theory\
n\n\nAbstract\nI will discuss some twisted variants of the GGP restriction
problems in the setting of skew-Hermitian spaces. Together with Gross and
Prasad\, we formulate conjectural answers to these twisted GGP problems a
nd provide some evidences in low rank and for unitary principal series.\n
LOCATION:https://researchseminars.org/talk/AIM-RTNCG-SemRepTh/3/
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BEGIN:VEVENT
SUMMARY:Binyong Sun (Zhejiang University)
DTSTART;VALUE=DATE-TIME:20210909T070000Z
DTEND;VALUE=DATE-TIME:20210909T075000Z
DTSTAMP;VALUE=DATE-TIME:20220528T192235Z
UID:AIM-RTNCG-SemRepTh/4
DESCRIPTION:Title: Archimedean period relations and period relations for automorph
ic L-functions\nby Binyong Sun (Zhejiang University) as part of Semina
r in Representation Theory\n\n\nAbstract\nIt was known to Euler that $\\ze
ta(2k)$ is a rational multiple of $\\pi^{2k}$\, where $\\zeta$ is the Eule
r--Riemann zeta function\, and $k$ is a positive integer. Following the pi
oneering works of G. Shimura\, P. Deligne and etc.\, D. Blasius proposed a
conjecture which asserts that similar rationality results hold for very g
eneral automorphic L-functions. We confirm Blasius's conjecture in two cas
es: the standard L-functions of symplectic type (joint with Dihua Jiang an
d Fangyang Tian)\, and the Rankin-Selberg L-functions for $\\operatorname{
GL}(n)\\times\\operatorname{GL}(n-1)$ (joint with Jian-Shu Li and Dongwen
Liu). The key ingredient is the Archimedean period relations for the modul
ar symbols at infinity. These two cases have already been studied by many
authors\, including Harris--Lin\, Grobner--Raghuram\, Harder--Raghuram\, J
anuszewski\, Grobner--Lin\, and etc.\n
LOCATION:https://researchseminars.org/talk/AIM-RTNCG-SemRepTh/4/
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SUMMARY:Yoshiki Oshima (Osaka University)
DTSTART;VALUE=DATE-TIME:20210909T081000Z
DTEND;VALUE=DATE-TIME:20210909T090000Z
DTSTAMP;VALUE=DATE-TIME:20220528T192235Z
UID:AIM-RTNCG-SemRepTh/5
DESCRIPTION:Title: On the asymptotic support of Plancherel measures for homogeneou
s spaces\nby Yoshiki Oshima (Osaka University) as part of Seminar in R
epresentation Theory\n\n\nAbstract\nLet $G$ be a real reductive group and
$X$ a homogeneous $G$-manifold. The Plancherel measure for $X$ describes h
ow $L^2(X)$ breaks up into irreducible unitary representations of $G$. We
discuss asymptotics of the support of Plancherel measure and relate it wit
h geometry of coadjoint orbits. In particular\, we give a sufficient condi
tion for the existence of discrete series. This is a joint work with Benja
min Harris.\n
LOCATION:https://researchseminars.org/talk/AIM-RTNCG-SemRepTh/5/
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