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SUMMARY:Reduction of symplectic symmetric spaces and étale affine represe
ntations
DTSTART;VALUE=DATE-TIME:20181019T083000Z
DTEND;VALUE=DATE-TIME:20181019T092000Z
DTSTAMP;VALUE=DATE-TIME:20210511T140020Z
UID:indico-contribution-3782-3290@indico.math.cnrs.fr
DESCRIPTION:Speakers: Yannick Voglaire (Université du Luxembourg)\nWe int
roduce a notion of symplectic reduction for symplectic symmetric spaces as
a means to the study of their structure theory. We show that any such sp
ace can be written as a direct product of a semisimple and a completely sy
mplectically reducible one. Underlying symplectic reduction is a notion of
so-called pre-Lie triple system. We will explain how these are related to
étale affine representations of Lie triple systems\, how any symplectic
symmetric space and any Jordan triple system yield such a structure\, and
how they allow to build new from old (symplectic) symmetric spaces.\n\nhtt
ps://indico.math.cnrs.fr/event/3782/contributions/3290/
LOCATION:UFR Sciences Amphi 2
URL:https://indico.math.cnrs.fr/event/3782/contributions/3290/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A class of locally compact quantum groups arising from Kohn-Nirenb
erg quantization
DTSTART;VALUE=DATE-TIME:20181018T153000Z
DTEND;VALUE=DATE-TIME:20181018T162000Z
DTSTAMP;VALUE=DATE-TIME:20210511T140020Z
UID:indico-contribution-3782-3288@indico.math.cnrs.fr
DESCRIPTION:Speakers: Victor Gayral (Université de Reims Champagne-Ardenn
e)\nLocally compact quantum group (LCQG) in the setting of von Neumann alg
ebras (aka Kustermans-Vaes quantum groups)\, is believed to give the corre
ct notion of symmetries of quantum spaces (in the setting of operator alge
bras). While this theory is fast growing\, there are very few examples of
(non-compact) LCQG. \nIn this talk\, I will explain how the good old Kohn-
Nirenberg quantization allows to construct a new class of LCQG (and also w
hy the very good old Weyl quantization doesn’t work here).\nThis is a jo
int work (in progress) with Pierre Bieliavsky\, Lars Tuset and Sergiy Nesh
veyev.\n\nhttps://indico.math.cnrs.fr/event/3782/contributions/3288/
LOCATION:UFR Sciences Amphi 2
URL:https://indico.math.cnrs.fr/event/3782/contributions/3288/
END:VEVENT
BEGIN:VEVENT
SUMMARY:K-theory of group C*-algebras and the BGG complex
DTSTART;VALUE=DATE-TIME:20181018T143000Z
DTEND;VALUE=DATE-TIME:20181018T152000Z
DTSTAMP;VALUE=DATE-TIME:20210511T140020Z
UID:indico-contribution-3782-3287@indico.math.cnrs.fr
DESCRIPTION:Speakers: Pierre Julg (Université d'Orléans)\nThe Baum-Conne
s conjecture on the K-theory of group C*-algebras is a difficult open prob
lem since the beginning of the 1980’s. In the last 30 years a programme
has been developed to prove the Baum-Connes conjecture with coefficients f
or semi-simple Lie groups. The tools involved are: the flag manifolds\, th
e BGG complex\, and L2 cohomology of symmetric spaces.\n\nhttps://indico.m
ath.cnrs.fr/event/3782/contributions/3287/
LOCATION:UFR Sciences Amphi 2
URL:https://indico.math.cnrs.fr/event/3782/contributions/3287/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Does $"ax+b"$ stand for the solvable analogue of $SL_2(\\mathbb{R
})$ in deformation theory ?
DTSTART;VALUE=DATE-TIME:20181019T070000Z
DTEND;VALUE=DATE-TIME:20181019T075000Z
DTSTAMP;VALUE=DATE-TIME:20210511T140020Z
UID:indico-contribution-3782-3289@indico.math.cnrs.fr
DESCRIPTION:Speakers: Ali Baklouti (Université de Sfax (Tunisie))\nLet $G
$ be a Lie group\, $H$ a closed subgroup of $G$ and $\\Gamma$ a discontinu
ous subgroup for the homogeneous space $\\mathscr{X}=G/H$\, which means t
hat $\\Gamma$ is a discrete subgroup of $G$ acting properly discontinuousl
y and fixed point freely on $\\mathscr{X}$. For any deformation of $\\Gamm
a$\, the deformed discrete subgroup may fail to act discontinuously on $\\
mathscr{X}$\, except for the case when $H$ is compact. \nThe subject of th
e talk is to emphasize this specific issue and to deal with some questions
related to the geometry of the related parameter and deformation spaces\,
namely the local rigidity conjecture in the nilpotent setting. When $G$ i
s semi-simple\, the analogue of the Selberg-Weil-Kobayashi rigidity theor
em in the non-Riemannian setting is recorded\, especially the role of the
group $SL_2(\\mathbb{R})$ as a fake twin of the solvable $"ax+b"$ is also
discussed.\n\nhttps://indico.math.cnrs.fr/event/3782/contributions/3289/
LOCATION:UFR Sciences Amphi 2
URL:https://indico.math.cnrs.fr/event/3782/contributions/3289/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Poisson transforms adapted to BGG-complexes
DTSTART;VALUE=DATE-TIME:20181018T130000Z
DTEND;VALUE=DATE-TIME:20181018T135000Z
DTSTAMP;VALUE=DATE-TIME:20210511T140020Z
UID:indico-contribution-3782-3286@indico.math.cnrs.fr
DESCRIPTION:Speakers: Christoph Harrach (University of Vienna (Austria))\n
Let $G$ be a semisimple Lie group with finite centre\, $K$ a maximal compa
ct subgroup and $P$ a parabolic subgroup of $G$. We present a new construc
tion of Poisson transforms between vector bundle valued differential forms
on the homogeneous parabolic geometry $G/P$ and its corresponding Riemann
ian symmetric space $G/K$ which is tailored to the exterior calculus and c
an be fully described by invariant elements in finite dimensional represen
tations of reductive Lie groups. Furthermore\, we show how these transform
s are compatible with several invariant differential operators\, which ind
uce a strong connection between Bernstein-Gelfand-Gelfand complexes on $G/
P$ and twisted deRham complexes on $G/K$. Finally\, we consider the specia
l case of the real hyperbolic space and its conformal boundary and discuss
Poisson transforms of differential forms with values in the bundle associ
ated to the standard representation $\\mathbb{R}^{n+1\,1}$ of $G = SO(n+1\
,1)_0$.\n\nhttps://indico.math.cnrs.fr/event/3782/contributions/3286/
LOCATION:UFR Sciences Amphi 2
URL:https://indico.math.cnrs.fr/event/3782/contributions/3286/
END:VEVENT
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SUMMARY:Asymptotics of characters and associated cycles of Harish-Chandra
modules
DTSTART;VALUE=DATE-TIME:20181019T093000Z
DTEND;VALUE=DATE-TIME:20181019T102000Z
DTSTAMP;VALUE=DATE-TIME:20210511T140020Z
UID:indico-contribution-3782-3291@indico.math.cnrs.fr
DESCRIPTION:Speakers: Salah Mehdi (Université de Lorraine (Metz))\nAbstra
ct: We describe a translation principle for the Dirac index of virtual $({
\\mathfrak g}\,K)$-modules. To each coherent family of such modules we att
ach a polynomial\, on the dual of the compact Cartan subalgebra\, which ex
presses the dependence of the leading term in the Taylor expansion of the
character of the modules. Finally we will explain how this polynomial is r
elated to the multiplicities of the associated cycle of certain Harish-Cha
ndra modules. These results are joint with P. Pandžić\, D. Vogan and R.
Zierau.\n\nhttps://indico.math.cnrs.fr/event/3782/contributions/3291/
LOCATION:UFR Sciences Amphi 2
URL:https://indico.math.cnrs.fr/event/3782/contributions/3291/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Conformally covariant bi-differential operators for differential f
orms
DTSTART;VALUE=DATE-TIME:20181018T120000Z
DTEND;VALUE=DATE-TIME:20181018T125000Z
DTSTAMP;VALUE=DATE-TIME:20210511T140020Z
UID:indico-contribution-3782-3308@indico.math.cnrs.fr
DESCRIPTION:Speakers: Khalid Koufany (Université de Lorraine - Nancy)\nTh
e classical Rankin-Cohen brackets are bi-differential operators from $C^
\\infty(\\mathbb R)\\times C^\\infty(\\mathbb R)$ into $ C^\\infty(\\math
bb R)$. They are covariant for the diagonal action of ${\\rm SL}(2\,\\mat
hbb R)$ through principal series representations. We construct generalizat
ions of these operators\, replacing $\\mathbb R$ by $\\mathbb R^n\,$ the g
roup ${\\rm SL}(2\,\\mathbb R)$ by the group ${\\rm SO}_0(1\,n+1)$ viewed
as the conformal group of $\\mathbb R^n\,$ and functions by differential
forms.\n\nhttps://indico.math.cnrs.fr/event/3782/contributions/3308/
LOCATION:UFR Sciences Amphi 2
URL:https://indico.math.cnrs.fr/event/3782/contributions/3308/
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