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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Restrictions of discrete series to $ \mathfrak{sl}(2, \mathbf{R})$


Author: Jorge Vargas
Journal: Proc. Amer. Math. Soc. 117 (1993), 1187-1192
MSC: Primary 22E47
MathSciNet review: 1113650
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Abstract: We prove that the restriction to $ \mathfrak{s}\mathfrak{l}(2,\mathbb{R})$ of the underlying Harish-Chandra module of a Discrete Series representation of a noncompact simple Lie group has no $ \operatorname{sl} (2)$-irreducible subrepresentations unless it is holomorphic. We also give a characterization of the holomorphic Discrete Series.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1113650-0
PII: S 0002-9939(1993)1113650-0
Keywords: Restriction of discrete series
Article copyright: © Copyright 1993 American Mathematical Society