Speaker: Prof. Anne-Marie Aubert (CNRS)

Title: On tempered unipotent representations of $p$-adic reductive groups

Time: 15:30-16:30  June 4, 2026 (Thursday)

Place: MCM110

Abstract: Let $G$ be a split connected reductive group over a nonarchimedean field local field $F$. By using the explicit Langlands correspondence for unipotent representations of $p$-adic groups, we will define a certain space of tempered unipotent representations of $G$ and its pure inner twists.

This space admits a description in terms of compact pairs attached to semisimple elements of the Langlands dual group of $G$, which allows to define a natural involution on it.

We will next formulate, and illustrate on examples, a conjectural compatibility statement between this involution and an extension of Lusztig's nonabelian Fourier transform to disconnected finite reductive groups.

It is joint work with Dan Ciubotaru and Beth Romano.