A functoriality principle for blocks of p-adic linear groups

Abstract : Bernstein blocks of complex representations of p-adic reductive groups have been computed in a large amount of examples, in part thanks to the theory of types a la Bushnell and Kutzko. The output of these purely representation-theoretic computations is that many of these blocks are equivalent. The motto of this paper is that most of these coincidences are explained, and many more can be predicted, by a functoriality principle involving dual groups. We prove a precise statement for groups related to GL n , and then state conjectural generalizations in two directions : more general reductive groups and/or integral l-adic representations.
Type de document :
Pré-publication, Document de travail
2016
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https://hal.archives-ouvertes.fr/hal-01292727
Contributeur : Jean-Francois Dat <>
Soumis le : lundi 25 juillet 2016 - 15:30:59
Dernière modification le : mardi 11 octobre 2016 - 14:46:34
Document(s) archivé(s) le : mercredi 26 octobre 2016 - 11:17:21

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  • HAL Id : hal-01292727, version 2
  • ARXIV : 1603.07238

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INSMI | UPMC | IMJ | USPC

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Jean-François Dat. A functoriality principle for blocks of p-adic linear groups. 2016. 〈hal-01292727v2〉

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