On some representations of degenerate affine Hecke algebras of type $BC_{n}$

Details On some representations of degenerate affine Hecke algebras of type $BC_{n}$ On some representations of degenerate affine Hecke algebras of type $BC_{n}$

2008-10-05

arxiv.org/abs/0810.0791v1

Mathematics

Representation Theory

24 pages, Latex

Scientific paper

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.

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