Functors for unitary representations of classical real groups and affine Hecke algebras

2009/06/12 by Dan Ciubotaru, Ciubotaru, Dan, Peter E. Trapa +1
Mathematics · #22E47 #22E50 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:22E47 #msc:22E50

paper · pdf · doi:10.48550/arxiv.0906.2378

23 pages, 2 tables

arxiv created 2009/06/12 · arxiv updated 2009/12/01

Abstract

We define exact functors from categories of Harish-Chandra modules for certain real classical groups to finite-dimensional modules over an associated graded affine Hecke algebra with parameters. We then study some of the basic properties of these functors. In particular, we show that they map irreducible spherical representations to irreducible spherical representations and, moreover, that they preserve unitarity. In the case of split classical groups, we thus obtain a functorial inclusion of the real spherical unitary dual (with real infinitesimal character) into the corresponding p-adic spherical unitary dual.

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