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

Let $G=GL(N)$, $K=GL(p)\times GL(q)$, 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 $B_n$, 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.