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Transactions of the American Mathematical Society

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


Author: Anne-Marie Aubert
Journal: Trans. Amer. Math. Soc. 347 (1995), 2179-2189
MSC: Primary 22E50; Secondary 20G05, 20G25, 20G40
DOI: https://doi.org/10.1090/S0002-9947-1995-1285969-0
Erratum: Trans. Amer. Math. Soc. 348 (1996), 4687-4690.
MathSciNet review: 1285969
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1995-1285969-0
Keywords: Reductive algebraic groups over finite and $ p$-adic fields, Coxeter groups, representations
Article copyright: © Copyright 1995 American Mathematical Society

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