Tempered representations and K-theory

Tempered representations with unipotent parahoric restriction: a noncommutative geometry viewpoint

27 févr. 2025, 15:00

1h

Amphithéâtre Hermite (Institut Henri Poincaré)

Orateur

Prof. Anne-Marie Aubert (IMJ-PRG CNRS)

Description

The category of smooth representations of a $p$-adic group $G$ admits a decomposition into Bernstein blocks. With Paul Baum, Roger Plymen and Maarten Solleveld, we have formulated a conjecture which relates these blocks to (possibly twisted) extended quotients of complex algebraic varieties by finite groups.

In this talk, I will first introduce $p$-adic groups and some of their representations. Next, I will describe the conjecture in the case of tempered representations with unipotent parahoric restriction, focusing on its links with the generalized Springer correspondence for complex disconnected groups and its K-theoretical aspects. As an application, I will show how it can be used to describe the theta correspondence.