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 | References | Similar Articles | Additional Information

Abstract: In this paper, let be the dual pair . We will determine the composition series of the Howe quotients of which are lifts from one-dimensional unitary representations of and unitary lowest weight modules of . We will also determine the unitarizability of the subquotients. Our method also works for the dual pairs and .

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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.