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Unitary equivalences for reductive p-adic groups
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 135, Number 6, December 2013
- pp. 1633-1674
- 10.1353/ajm.2013.0048
- Article
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We establish a transfer of unitarity for a Bernstein component of the category of
smooth representations of a reductive $p$-adic group to the associated Hecke algebra,
in the framework of the theory of types, whenever the Hecke algebra is an affine Hecke
algebra with geometric parameters, in the sense of Lusztig (possibly extended by a group
of automorphisms of the root datum). It is known that there is a large class of such
examples (detailed in the paper). As a consequence, we establish relations between
the unitary duals of different groups, in the spirit of endoscopy.