  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.
