Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the unitary dual of the classical Lie groups,
Representations of $Sp(p,q)$

Author: Susana A. Salamanca-Riba
Journal: Proc. Amer. Math. Soc. 125 (1997), 3107-3117
MSC (1991): Primary 22E46, 22D10; Secondary 22E47, 20G05
MathSciNet review: 1401753
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Abstract: In this paper we prove that a unitary representation of $Sp(p,q)$ whose infinitesimal character satisfies some regularity condition is infinitesimally isomorphic to an $A_{\mathfrak {q}} \ (\lambda )$ module. This is done using similar techniques as those used by the author in earlier work.

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Additional Information

Susana A. Salamanca-Riba
Affiliation: Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003

Keywords: Real semisimple Lie groups, unitary representations, Zuckerman modules
Received by editor(s): October 10, 1995
Received by editor(s) in revised form: April 19, 1996
Additional Notes: Supported by NSF grant DMS–9108990
Communicated by: Roe Goodman
Article copyright: © Copyright 1997 American Mathematical Society