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Article Dans Une Revue Representation Theory Année : 2006

Algebres de Hecke affines generiques

Résumé

Let $H$ be a generic affine Hecke algebra (Iwahori-Matsumoto definition) over a polynomial algebra with a finite number of indeterminates over the ring of integers. We prove the existence of an integral Bernstein-Lusztig basis related to the Iwahori-Matsumoto basis by a strictly upper triangular matrix, from which we deduce that the center $Z$ of $H$ is finitely generated and that $H$ is a finite type $Z$-module (this was proved after inversion of the parameters by Bernstein-Lusztig), and we give some applications to the theory of $H$-modules where the parameters act by 0. These results are related to the smooth $p$-adic or mod $p$ representations of reductive $p$-adic groups. We introduce the supersingular modules of the affine Hecke algebra of GL(n) with parameter 0, probably analogues of the Barthel-Livne supersingular mod $p$ representations of GL(2).

Dates et versions

hal-00020493 , version 1 (11-03-2006)

Identifiants

Citer

Marie-France Vigneras. Algebres de Hecke affines generiques. Representation Theory, 2006, 10, pp.1-20. ⟨hal-00020493⟩
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