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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

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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
Represent. Theory 10 (2006), 21-47
Published electronically: January 9, 2006


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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Bibliographic Information
  • Soo Teck Lee
  • Affiliation: Department of Mathematics, National University of Singapore, 2, Science Drive, Singapore 117543
  • Email:
  • 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:
  • MathSciNet review: 2192485