DISCRETE DECOMPOSABILITY OF THE RESTRICTION OF AQ(LAMBDA) WITH RESPECT TO REDUCTIVE SUBGROUPS AND ITS APPLICATIONS

• 成果类型: Article
• 署名作者: KOBAYASHI, T
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/BF01232239
• 发表日期: 1994
• 页码: 181-205
• 关键词: series representations; standard modules; duality theorem; unitary; localization; SPACES

摘要

Let G' subset-of G be real reductive Lie groups and q a theta-stable parabolic subalgebra of Lie (G) x C. This paper offers a sufficient condition on (G, G', q) that the irreducible unitary representation A(q)BAR of G with non-zero continuous cohomology splits into a discrete sum of irreducible unitary representations of a subgroup G', 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 where Aq is not necessarily a highest weight module.