Unitary equivalences for reductive p-adic groups

2009/09/28 by Dan Barbasch, Barbasch, Dan, Dan Ciubotaru +1
Mathematics · #22E50 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.0909.5241

openalex publication_date 2009/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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