ESI Programme on
Representation Theory of Reductive Groups -Local and Global Aspects

January 4 - February 28 2009

Workshop: January 25-February 6

All abstracts for the period January 2- February 28

(download)

schedule for the first week (January 26-30) (download)

schedule for the second week (February 2-6) (download)

Organising Committee

Guy Henniart (U Paris XI)
Goran Muić (U Zagreb)
Joachim Schwermer (U Vienna)

Overview Programme List of Participants



Overview

This program "Representation Theory of Reductive Groups - Local and Global Aspects" will focus on several aspects of the theory of automorphic representations. That theory possesses a very strong structure given by the Langlands program, in particular, the functoriality principle. This involves Galois or Weil group representations, the representation theory of local reductive groups, and questions regarding automorphic spectra. Recently there have been important developments which we intend to cover as well as current research.


Programme

One of the main goals in number theory is to understand the absolute Galois group Galk of a local or global field k. In the case of an algebraic number field, Artin attached to every finite dimensional representation its L-function, a complex analytic invariant. The study of the finite dimensional representation theory of Galk via these Artin L-functions represents one approach to understand the absolute Galois group in this case. Though these L - functions turned out to be fundamental in formulating and proving Artin's general reciprocity law, the crowning achievement of abelian class field theory, they served as well as essential ingredients in the search for a non-abelian class field theory. Parallel to this development, there are the L-functions of Hecke. Nowadays, these have to be viewed as special cases of L-functions attached to automorphic representations of the general linear group over the ring of adeles of k.

It is one of the pillars of what is now known as the Langlands program that there exists a correspondence between the n- dimensional representations of Galk and the automorphic representations of GLn( A) which preserves the corresponding L- functions. More precisely, given a reductive group G there is the complex dual group LG, and the conjectures by Langlands predict natural correspondences between admissible homomorphisms of the Weil group Wk ( a generalization of the absolute Galois group) into the dual group and automorphic representations of G(A) and compatible local correspondences between admissible homomorphisms of the local Weil group of kv into the dual group and admissible representations of G(kv ) where kv denotes the local field associated to a place v of the number field k . One can view this as an arithmetic parametrization of automorphic representations. If one views the passage of information from the automorphic side to the Galois (or L-group) side, this is a global or local non-abelian class field theory.

The principle of functoriality forms another pillar of the Langlands program. This principle is associated to what is called an L-group homomorphism between the L-groups attached to given reductive groups G and H. Whenever one has such a homomorphism, one should expect a strong relationship between automorphic representations of the two groups. This transfer of automorphic representations is encoded in the Langlands correspondence and mediated by an equality of Artin L-functions.

Since its first formulation in 1968, there has been significant progress made in the understanding of the many facets of the Langlands program. It would lead us too far astray to discuss the results in detail. (We refer , for example, to some detailed surveys and works in Automorphic Representations, L-functions, and Applications: Progress and Prospects, ed. by J. Cogdell et al., de Gruyter 2005.)

This programme "Representation Theory of Reductive Groups - Local and Global Aspects" will focus on several aspects of the theory of automorphic representations. That theory possesses a very strong structure given by the Langlands programme, in particular, the functoriality principle. This involves Galois or Weil group representations, the representation theory of local reductive groups, and questions regarding automorphic spectra. Recently there have been important developments which we intend to cover as well as current research. We list some of them:


(A) Local Aspects of Automorphic Representations:

-construction of L-packets and A-packets for classical and exceptional groups.

- models of representations and construction of automorphic L--functions out of them.

-unitarity of representations.


(B) Representations of Reductive p-adic Groups:

- the theory of types

- R-representations

- mod p and p-adic representations

The programme will combine series of lectures on recent developments with ample time for informal discussions and collaborations over a longer period of time.

List of participants

Stephen Kudla (Toronto)
Marcela Hanzer (Zagreb)
Shaun Stevens (Norwich)
Marie France Vigneras (Paris)
Colette Moeglin (Paris)
Peter Schneider (Muenster)
Alberto Minguez (Paris)
Gordan Savin (Salt Lake City)
Colin Bushnell (London)
Erez Lapid (Jerusalem)
Harald Grobner (Vienna)
Ioan Badulescu (Montpellier)
Dipendra Prasad (Bombay)
Michael Rapoport (Bonn)
Juergen Rohlfs (Eichstatt)
Freydoon Shahidi (West Lafayette)
Corinne Blondel (Paris)
Volker Heiermann (Aubiere)
Henri Carayol (Strasburg)
Allen Moy (Hong-Kong)
Takayuki Oda (Tokyo)
Takahiro Hayata (Yamagata)
Samuel Patterson (Goettingen)
Guido Kings (Regensburg)
Vincente Secherre (Marseille)
Guy Henniart (Paris)
Jim Cogdell (Columbus)
Guenter Harder (Bonn)
Marko Tadic (Zagreb)
Dihua Jiang (Minnesota)
Neven Grbac (Zagreb)
Don Blasius (Los Angeles)
Mahdi Asgari (Stillwater)
Stephen Rallis (Columbus)
Chris Jantzen (Greenville)
Elmar Grosse-Kloenne(Berlin)
Jean-Pierre Labesse (Marseille)
Muthu Krishnamurthy (Iowa)
Joachim Schwermer (Vienna)
A. Raghuram (Stillwater)
Mark Reeder (Boston)
Ivan Matic (Osijek)
Drazen Adamovic (Zagreb)
Mirko Primc (Zagreb)
Goran Muic (Zagreb)