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.
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Contributor : Jean-Francois Dat <>
Submitted on : Monday, July 25, 2016 - 3:30:59 PM
Last modification on : Thursday, April 4, 2019 - 1:24:42 AM
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  • HAL Id : hal-01292727, version 2
  • ARXIV : 1603.07238


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



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