Institut de Mathématiques de Luminy

GROUPE DE TRAVAIL 2005
groupes réductifs

Organisateurs : Patrick Delorme, Jean-Pierre Labesse, Ctirad Klimcik
Salle Séminaires : 3 ème étage, pièce 306, I.M.L., Groupe des Laboratoires de Luminy (CNRS).

Planning

mardi 13 décembre
à 15h00
Roberto Miatello (Univ. Cordoba, Argentine) :
Some formulas and densities of automorphic forms for Hilbert modular groups.

JOURNEE SPECIALE

jeudi 8 décembre

14h30-15h30
Anton Alekseev (Geneva) :
The Gelfand-Zeitlin integrable system
and the Flaschka-Ratiu conjecture.

Abstract: Let G be a compact connected Lie group. By the Ginzburg-Weinstein theorem, there is a Poisson isomorphism between the space g^* (with Kirillov-Kostant-Souriau bracket) and the dual Poisson-Lie group G^* (with Lu-Weinstein bracket). In 1995, Flaschka and Ratiu conjectured that in the case of G=U(n) there is a Ginzburg-Weinstein isomorphism intertwining the Gelfand-Zeitlin completely integrable systems on g^* and G^*. I'll report on the proof of this conjecture. In particular, this result gives an explicit construction of a Ginzburg-Weinstein isomorphism for G=U(n) and n>2.

15h30-16h30
Tudor Ratiu (Lausanne) :
Banach Poisson manifolds
and geometric representation theory.

Abstract: Banach Poisson manifolds are objects that appear in many physical applications. After introducing these objects, special emphasis will be given to the Lie-Poisson case. Coadjoint orbits will be discussed and their geometry linked to von Neumann algebras.
The first steps towards a geometric representation theory will be presented.

17h00-18h00
Rita Fioresi (Bologna) :
Algebraic Supergroups and their Homogeneous Spaces.

Abstract: The notion of algebraic superscheme and supergroup can be introduced via their functor of points. This point of view helps to recover part of the geometric intuition otherwise lost in the superalgebraic setting. In this framework it is possible for example to associate naturally to a given algebraic supergroup a Lie superalgebra, which is identified with the tangent superspace to the supergroup at the identity. We want to discuss in some specific examples how it is possible to describe quotients of algebraic and Lie supergroups and the problems involved in such definitions in general.

jeudi 24 novembre
à 15h30
Vincent Sécherre (IML) :
Méthodes immobilières dans l'étude des espaces symétriques p-adiques.

mercredi 7 septembre
à 14h30
Joseph Bernstein (Univ. Tel Aviv) :
Periods of automorphic functions, subconvexity
of L-functions and representation theory.
(joint work in progress with Andre Reznikov).

lundi 27 juin
à 14h30
Eric Opdam (Univ. Amsterdam) :
Singularities at the boundary of the crown domain
(joint work in progress with Bernhard Kroetz).

Abstract: The crown domain $\Xi$ of a Riemannian symmetric space $X$ is a $G$-invariant domain of holomorphy in the complexification $X_\mathbb{C}$ of $X$ which is maximal with respect to the property that every elementary spherical function on X extends to a holomorphic function $\Xi$.
Knowledge of the singularities of (the extensions of) the elementary spherical functions at the boundary of $\Xi$ has several interesting applications, for example to estimates of triple products of Maass forms (following ideas of Sarnak, Bernstein-Reznikov,
and Kroetz-Stanton).
We describe in this talk the geometry of the closed $G$-orbits in the boundary of $\Xi$. We then use Dunkl-Cherednik theory and monodromy arguments in order to compute the leading terms in the singular expansion of the elementary spherical function at the extremalboundary points of $\Xi$.

jeudi 9 juin
à 14h30
Dan Barbasch (Univ. Cornell) :
Unitary parameters for principal series
of split real and p-adic groups.

jeudi 12 mai
à 14h
Patrick Delorme (IML) :
Algèbre de Schwartz d'une algèbre de Hecke affine.

jeudi 28 avril
à 14h
Vincent Sécherre (IML) :
Types simples pour GL(m,D).

lundi 24 janvier
Nicolas Bergeron (Orsay) :
Propriétés de Lefschetz automorphes.

Historique : [ 2003 ] [ 2004 ]

Last update : december 6, 2005, EL.