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Inventiones mathematicae

, Volume 117, Issue 1, pp 181–205 | Cite as

Discrete decomposability of the restriction ofAq(λ) with respect to reductive subgroups and its applications

  • Toshiyuki Kobayashi
Article

Summary

LetG′⊂G be real reductive Lie groups and q a θ-stable parabolic subalgebra of Lie (G) ⊗ ℂ. This paper offers a sufficient condition on (G, G′, q) that the irreducible unitary representation\(\mathop {A_q }\limits^--- \) ofG with non-zero continuous cohomology splits into a discrete sum of irreducible unitary representations of a subgroupG′, each of finite multiplicity. As an application to purely analytic problems, new results on discrete series are also obtained for some pseudo-Riemannian (non-symmetric) spherical homogeneous spaces, which fit nicely into this framework. Some explicit examples of a decomposition formula are also found in the cases whereAq is not necessarily a highest weight module.

Keywords

High Weight Homogeneous Space Unitary Representation Analytic Problem Weight Module 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Toshiyuki Kobayashi
    • 1
  1. 1.Department of Mathematical SciencesUniversity of TokyoTokyoJapan

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