2008/10/05 by Xiaoguang Ma, Ma, Xiaoguang · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT
paper · pdf · doi:10.48550/arxiv.0810.0791
24 pages, Latex
arxiv created 2008/10/05 · openalex publication_date 2008/10/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Bn. 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 yi. In the rank 1 case, we write down an explicit formula for the generator y1 in terms of central elements of U(g) and calculate the eigenvalue of y1 by using the central characters.