Dualité dans le groupe de Grothendieck de la catégorie des représentations lisses de longueur finie d’un groupe réductif 𝑝-adique

Aubert, Anne-Marie

doi:10.1090/S0002-9947-1995-1285969-0

Dualité dans le groupe de Grothendieck de la catégorie des représentations lisses de longueur finie d’un groupe réductif $p$-adique
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by Anne-Marie Aubert

Trans. Amer. Math. Soc. 347 (1995), 2179-2189

DOI: https://doi.org/10.1090/S0002-9947-1995-1285969-0

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Erratum: Trans. Amer. Math. Soc. 348 (1996), 4687-4690.

Abstract:

We define an involution on the Grothendieck ring of the category of finite length smooth representations of a $p$-adic algebraic group, which is a direct analogue Curtis-Alvis duality for finite groups of Lie type. This involution commutes with taking the contragredient, with parabolic induction and, up a few twists, with truncation. It also preserves the irreducible representations up to sign.

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