A Lie-theoretic construction of some representations of the degenerate affine and double affine Hecke algebras of type BCn

Abstract

Let G=GL(N), K=GL(p) x GL(q), where p+q=N, and let n be a positive integer. We construct a functor from the category of Harish-Chandra modules for the pair (G,K) to the category of representations of the degenerate affine Hecke algebra of type B_n [B subscript n], and a functor from the category of K-monodromic twisted D-modules on G/K to the category of representations of the degenerate double affine Hecke algebra of type BC_n [BC subscript n]; the second functor is an extension of the first one.