On endomorphism algebras of Gelfand-Graev representations II

Abstract

Let $G$ be a connected reductive group defined over a finite field ${\mathbb{F}}_q$ of characteristic $p$, with Deligne--Lusztig dual $G^{\ast }$. We show that, over $\overline{\mathbb{Z}}[1/pM]$ where $M$ is the product of all bad primes for $G$, the endomorphism ring of a Gelfand--Graev representation of $G({\mathbb{F}}_q)$ is isomorphic to the Grothendieck ring of the category of finite-dimensional ${\overline{\mathbb{F}}}_q$-representations of $G^{\ast }({\mathbb{F}}_q)$.

15 pages. The section numbering has been changed

Cited by in corpus (1)

• Irreducible components of the moduli space of Langlands parameters