The Gelfand--Graev representation of SO$(2n+1)$ in terms of Hecke algebras

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 $G=$SO$(2n+1)$.