On endomorphism algebras of Gelfand–Graev representations II

Abstract

AbstractLet be a connected reductive group defined over a finite field of characteristic , with Deligne–Lusztig dual . We show that, over where is the product of all bad primes for , the endomorphism ring of a Gelfand–Graev representation of is isomorphic to the Grothendieck ring of the category of finite‐dimensional ‐representations of .