Tempered representations with unipotent parahoric restriction: a noncommutative geometry viewpoint
Appears in collection : 2025 - T1 - WS2 - Tempered representations and K-theory
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.
