Speaker: Prashant Arote, IISER Pune.

Title: Harish-Chandra Induction and Jordan Decomposition of Characters
 
Abstract:
 Let G be a connected reductive group defined over a finite field 𝔽q and let
F:G→ G be the corresponding Frobenius morphism.
Let L be a Levi factor of a F-stable parabolic subgroup of G.
Endomorphism algebras of  representations parabolically induced from cuspidal representations
 of LF were described by Howlett and Lehrer.
In this talk, we show that any such algebra is isomorphic to the twisted endomorphism algebra
of a representation which is parabolically induced from a unipotent cuspidal representation of
 Levi subgroup of a finite reductive group.
As an application, we show that for any finite connected reductive group, a Jordan decomposition
can be chosen such that it commutes with Harish-Chandra induction.
This is a joint work with Manish Mishra.