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Restrictions of Discrete Series to sl(2, R)

Jorge Vargas
Proceedings of the American Mathematical Society
Vol. 117, No. 4 (Apr., 1993), pp. 1187-1192
DOI: 10.2307/2159550
Stable URL: http://www.jstor.org/stable/2159550
Page Count: 6
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Restrictions of Discrete Series to sl(2, R)
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Abstract

We prove that the restriction to sl(2, R) of the underlying Harish-Chandra module of a Discrete Series representation of a noncompact simple Lie group has no sl(2)-irreducible subrepresentations unless it is holomorphic. We also give a characterization of the holomorphic Discrete Series.

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