On some representations of degenerate affine Hecke algebras of type $B{C}_n$

Abstract

Let G=U(p,q) and K=U(p)xU(q). In arXiv:0801.1530, the authors 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. In this paper, we study the image of the principal series modules of G under this functor. We describe the dAHA module structure of the image by constructing a family of common eigenvectors of {y_i}. In the rank 1 case, we write down an explicit formula for the generator y_{1} in terms of central elements of U(g) and calculate the eigenvalue of y_{1} by using the central characters.

arXiv comment24 pages, Latex

References in corpus (1)

• A Lie-theoretic construction of representations of the degenerate affine and double affine Hecke algebras of type $B{C}_n$

Cited by in corpus (4)

• A Lie-theoretic construction of representations of the degenerate affine and double affine Hecke algebras of type $B{C}_n$
• Duality between GL(n,R) and the degenerate affine Hecke algebra for gl(n)
• Functors for unitary representations of classical real groups and affine Hecke algebras
• Representations of Degenerate Affine Hecke Algebra of Type $C_n$ Under the Etingof-Freund-Ma Functor