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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Howe quotients of unitary characters and unitary lowest weight modules
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by Hung Yean Loke; with an Appendix by Soo Teck Lee PDF
Represent. Theory 10 (2006), 21-47 Request permission

Abstract:

In this paper, let $(G,Gโ€™)$ be the dual pair $(\widetilde {\mathrm {Sp}}(p,\mathbb {R}), \tilde {\mathrm O}(n,m))$. We will determine the composition series of the Howe quotients of $Gโ€™$ which are lifts from one-dimensional unitary representations of $G$ and unitary lowest weight modules of $G$. We will also determine the unitarizability of the subquotients. Our method also works for the dual pairs $(\widetilde {\mathrm U}(p,q), \widetilde {\mathrm U}(n,m))$ and $(\tilde {\mathrm O}^*(2p), \widetilde {\mathrm {Sp}}(n,m))$.
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Additional Information
  • Soo Teck Lee
  • Affiliation: Department of Mathematics, National University of Singapore, 2, Science Drive, Singapore 117543
  • Email: matlhy@nus.edu.sg
  • Received by editor(s): March 8, 2005
  • Received by editor(s) in revised form: September 13, 2005
  • Published electronically: January 9, 2006
  • Additional Notes: The research of Hung Yean Loke was partially funded by the NUS Academic Research Grant R-146-000-026-112
    The research of Soo Teck Lee was partially funded by the NUS Academic Research Grant R-146-000-026-112
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 10 (2006), 21-47
  • MSC (2000): Primary 22E46, 22E47
  • DOI: https://doi.org/10.1090/S1088-4165-06-00279-2
  • MathSciNet review: 2192485