Abstract

Let k be a p-adic field with involution σ0 and let k0 be its fixed subfield of k. Let V be a finite dimensional vector space defined over k equipped with ε-Hermitian form < , >. Let G be the connected component of the group of isometries on (V, < , >). In order to understand the admissible representations of G, we construct a large family of Hecke algebras on G. In fact, we conjecture that all admissible representations of G arise in our construction. As a corollary of this construction, we also get many (possibly all) supercuspidal representations. Our constructions are valid when the residue characteristic of k0 is large.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 967-1029
Launched on MUSE
1999-10-01
Open Access
No
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