A Lie-theoretic construction of some representations of the degenerate affine and double affine Hecke algebras of type 𝐵𝐶_{𝑛}

Abstract

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