Israel Journal of Mathematics

, Volume 137, Issue 1, pp 355–379 | Cite as

Degenerate principal series representations of Sp(p, q)

  • Soo Teck Lee
  • Hung Yean Loke


Letp>q and letG=Sp(p, q). LetP=LN be the maximal parabolic subgroup ofG with Levi subgroupL≅GL q (ℍ)×Sp(pq). Forsεℂ andμ a highest weight of Sp(pq), let пs,µ be the representation ofP such that its restriction toN is trivial and\(\pi s,\mu |L = \det _q^s \)T p-q μ , where det q is the determinant character of GL q (ℍ) andT p-q μ is the irreducible representation of Sp(pq) with highest weightμ. LetI p,q(s, μ) be the Harish-Chandra module of the induced representation Ind P G \(\begin{array}{*{20}c} G \\ P \\\end{array}\pi _{s,\mu } \). In this paper, we shall determine the module structure and unitarity ofI p, q(s, μ).


Module Diagram Main Lemma High Weight Vector Levi Subgroup Finite Dimensional Representation 
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© Hebrew University 2003

Authors and Affiliations

  • Soo Teck Lee
    • 1
  • Hung Yean Loke
    • 1
  1. 1.Department of MathematicsNational University of SingaporeSingapore

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