Opérateurs d'entrelacement et algèbres de Hecke avec paramètres d'un groupe réductif $p$-adique - le cas des groupes classiques

Abstract

For $G$ a symplectic or orthogonal $p$-adic group (not necessarily split), or an inner form of a general linear $p$-adic group, we compute the endomorphism algebras of some induced projective generators à la Bernstein of the category of smooth representations of $G$ and show that these algebras are isomorphic to the semi-direct product of a Hecke algebra with parameters by a finite group algebra. Our strategy and parts of our intermediate results apply to a general reductive connected $p$-adic group.

44 pages in French; added translation in English by Yujie Xu