Mathematics – Representation Theory
Scientific paper
2008-04-28
Mathematics
Representation Theory
40 pages; compatibility with parabolic induction added, following a suggestion of an unknown referee
Scientific paper
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 \`a 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.
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