en fr The ℓ-modular Zelevinski involution Linvolution de Zelevinski modulo ℓ Report as inadecuate




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1 IMJ - Institut de Mathématiques de Jussieu 2 LMV - Laboratoire de Mathématiques de Versailles

Abstract : Let F be a non-Archimedean locally compact field with residual characteristic p, let G be an inner form of GLn,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.

Keywords : p-adic reductive groups type theory finite reductive groups Zelevinski involution Alvis-Curtis duality Modular representations





Author: Alberto Mínguez - Vincent Sécherre -

Source: https://hal.archives-ouvertes.fr/



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