A functoriality principle for blocks of p-adic linear groups

2016/03/23 by Jean-François Dat, Dat, Jean-François
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1603.07238

openalex publication_date 2016/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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