A Lie-theoretic construction of representations of the degenerate affine   and double affine Hecke algebras of type $BC_n$
  Let G=GL(N), K=GL(p)xGL(q), where p+q=N, and 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, 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; the second functor is an extension of the first one. These functors are generalizations of the type A functors from q-alg/9710037 and math/0702670, respectively. 
Pavel Etingof, Rebecca Freund, Xiaoguang Ma