A functoriality principle for blocks of p-adic linear groups

Jean-François Dat (1)

1 IMJ - Institut de Mathématiques de Jussieu

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.

Mots clés: p-adic groups; blocks; Langlands functoriality

Domaines: Théorie des représentations [math.RT]; Théorie des nombres [math.NT]

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