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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
Article

Abstract

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).

Keywords

Module Diagram Main Lemma High Weight Vector Levi Subgroup Finite Dimensional Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© 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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