## 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 - DOI: https://doi.org/10.1090/S1088-4165-06-00279-2
- Published electronically: January 9, 2006
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## 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 $(\tilde {\mathrm O}^*(2p), \widetilde {\mathrm {Sp}}(n,m))$.## References

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## Bibliographic 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