The Gelfand–Graev representation of classical groups in terms of Hecke algebras

Abstract

Abstract Let G be a p-adic classical group. The representations in a given Bernstein component can be viewed as modules for the corresponding Hecke algebra—the endomorphism algebra of a pro-generator of the given component. Using Heiermann’s construction of these algebras, we describe the Bernstein components of the Gelfand–Graev representation for $G=\mathrm {SO}(2n+1)$ , $\mathrm {Sp}(2n)$ , and $\mathrm {O}(2n)$ .