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), 2147 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 onedimensional 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 $(\tilde {\mathrm O}^*(2p), \widetilde {\mathrm {Sp}}(n,m))$.References

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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 R146000026112
The research of Soo Teck Lee was partially funded by the NUS Academic Research Grant R146000026112  © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.  Journal: Represent. Theory 10 (2006), 2147
 MSC (2000): Primary 22E46, 22E47
 DOI: https://doi.org/10.1090/S1088416506002792
 MathSciNet review: 2192485