Irreducible representations of p-adic linear groups

Date: 
Thursday, November 12, 2015 - 3:30pm
Location: 
111 MSB
Speaker: 
Alberto Minguez (Institut de Mathematiques de Jussieu)

Abstract: One of the cornerstones of the representation theory of 
reductive groups over non-archimedean local fields is the seminal work 
of Bernstein and Zelevinsky in the 1970s. Much of their work is 
concentrated on the general linear group. It culminated in Zelevinsky's 
classification of the (complex, smooth) irreducible
representations of $GL_n(F)$ (where $F$ is a non-archimedean local 
field) in terms of multisegments --
an almost purely combinatorial object. Later on this classification was 
extended to inner forms of the general linear groups, namely to the 
groups $GL_n(D)$ where $D$ is a local non-archimedean division algebra. 
There are two classification schemes, "à la Zelevinsky" and "à la 
Langlands". The Langlands classification is  valid for any reductive 
group, but in the case of linear groups it can be refined and made more 
explicit.

In this talk we will explain these classifications and a new approach, 
due to Lapid-Minguez-Tadic, giving a uniform proof of the 
classifications in all cases.

Event Type: