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

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.

23 pages, 2 tables

References in corpus (4)

• Unitary spherical spectrum for split classical groups
• On some representations of degenerate affine Hecke algebras of type $B{C}_n$
• A Lie-theoretic construction of representations of the degenerate affine and double affine Hecke algebras of type $B{C}_n$
• Duality between GL(n,R) and the degenerate affine Hecke algebra for gl(n)

Cited by in corpus (1)

• Dirac cohomology for graded affine Hecke algebras