Duality between GL(n,R) and the degenerate affine Hecke algebra for gl(n)

Abstract

We define an exact functor $F_{n,k}$ from the category of Harish-Chandra modules for $GL(n,R)$ to the category of finite-dimensional representations for the degenerate affine Hecke algebra for $gl(k)$. Under certain natural hypotheses, we prove that the functor maps standard modules to standard modules (or zero) and irreducibles to irreducibles (or zero).

22 pages

References in corpus (2)

• Unitary spherical spectrum for split classical groups
• On some representations of degenerate affine Hecke algebras of type $B{C}_n$

Cited by in corpus (1)

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