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Howe quotients of unitary characters and unitary lowest weight modules


Author: Hung Yean Loke; with an Appendix by Soo Teck Lee
Journal: Represent. Theory 10 (2006), 21-47
MSC (2000): Primary 22E46, 22E47
DOI: https://doi.org/10.1090/S1088-4165-06-00279-2
Published electronically: January 9, 2006
MathSciNet review: 2192485
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Abstract: In this paper, let $ (G,G')$ 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 $ G'$ 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

DOI: https://doi.org/10.1090/S1088-4165-06-00279-2
Keywords: Howe quotients, local theta lifts, unitary characters, unitary lowest weight modules, composition series
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
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.