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Article Dans Une Revue Representation theory Année : 2015

The ℓ-modular Zelevinski involution

L'involution de Zelevinski modulo ℓ

Résumé

Let F be a non-Archimedean locally compact field with residual characteristic p, let G be an inner form of GL(n,F) for a positive integer n and let R be an algebraically closed field of characteristic different from p. When R has characteristic ℓ>0, the image of an irreducible smooth R-representation π of G by the Aubert involution need not be irreducible. We prove that this image (in the Grothendieck group of G) contains a unique irreducible term π* with the same cuspidal support as π. This defines an involution on the set of isomorphism classes of irreducible R-representations of G, that coincides with the Zelevinski involution when R is the field of complex numbers. The method we use also works for F a finite field of characteristic p, in which case we get a similar result.
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Dates et versions

hal-01133755 , version 1 (20-03-2015)

Identifiants

Citer

Alberto Mínguez, Vincent Sécherre. L'involution de Zelevinski modulo ℓ. Representation theory, 2015, 19. ⟨hal-01133755⟩
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