Inventiones mathematicae

, Volume 117, Issue 1, pp 181–205

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

  • Toshiyuki Kobayashi
Article

DOI: 10.1007/BF01232239

Cite this article as:
Kobayashi, T. Invent Math (1994) 117: 181. doi:10.1007/BF01232239

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.

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

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