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On the unitary dual of the classical Lie groups, Representations of 
Author(s):
Susana
A.
Salamanca-Riba
Journal:
Proc. Amer. Math. Soc.
125
(1997),
3107-3117.
MSC (1991):
Primary 22E46, 22D10;
Secondary 22E47, 20G05
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Abstract:
In this paper we prove that a unitary representation of  whose infinitesimal character satisfies some regularity condition is infinitesimally isomorphic to an  module. This is done using similar techniques as those used by the author in earlier work.
References:
- 1.
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- 2.
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 -types of the irreducible unitary  -modules with non-zero relative cohomology. Invent. Math. 59 (1980) 1-11. MR 83c:17011 - 3.
- R. Parthasarathy, Criteria for the unitarizability of some highest weight modules. Proc. Indian Acad. Sci. 89 (1980) 1-24. MR 82c:22020
- 4.
- S. A. Salamanca-Riba, On the unitary dual of some classical Lie groups. Compositio Mathematica. 68 (1988) 251-303 MR 89m:22018
- 5.
- S. A. Salamanca-Riba, On the unitary dual of the classical Lie groups II. Representations of SO(n,m) inside the dominant Weyl chamber. Compositio Mathematica. 86 (1993) 127-146. MR 94e:22025
- 6.
- D. A. Vogan Jr., The algebraic structure of the representations of semisimple Lie groups I. Annals of Mathematics. 109 (1979) 1-60. MR 81j:22020
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Additional Information:
Susana
A.
Salamanca-Riba
Affiliation:
Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003
Email:
ssalaman@nmsu.edu
DOI:
10.1090/S0002-9939-97-03932-4
PII:
S 0002-9939(97)03932-4
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
Copyright of article:
Copyright
1997,
American Mathematical Society
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