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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Generic representations are induced from square-integrable representations


Author: Ronald L. Lipsman
Journal: Trans. Amer. Math. Soc. 285 (1984), 845-854
MSC: Primary 22E45
MathSciNet review: 752506
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Abstract: It is proven for arbitrary real algebraic groups that the generic irreducible unitary representation is induced from a square-integrable representation (modulo the projective kernel). This generalizes the well-known result for reductive groups that the generic representations are either discrete series, or induced from discrete series (modulo the nilradical) representations of cuspidal parabolic subgroups.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1984-0752506-9
PII: S 0002-9947(1984)0752506-9
Article copyright: © Copyright 1984 American Mathematical Society