Discrete decomposability of the restriction of Aq(λ) with respect to reductive subgroups - III. Restriction of Harish-Chandra modules and associated varieties

• 成果类型: Article
• 署名作者: Kobayashi, T
• 署名单位: University of Tokyo
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s002220050203
• 发表日期: 1998
• 页码: 229-256
• 关键词: differential-operators; homogeneous spaces; REPRESENTATIONS; series

摘要

Let H subset of G be real reductive Lie groups and pi an irreducible unitary representation of G. We introduce an algebraic formulation (discretely decomposable restriction) to single out the nice class of the branching problem (breaking symmetry in physics) in the sense that there is no continuous spectrum in the irreducible decomposition of the restriction pi/(H). This paper offers basic algebraic properties of discretely decomposable restrictions, especially for a reductive symmetric pair (G,H) and for the Zuckerman-Vogan derived functor module pi = <(A(q)((lambda))over bar>, and proves that the sufficient condition [Invent. Math.'94] is in fact necessary. A finite multiplicity theorem is established for discretely decomposable modules which is in sharp contrast to known examples of the continuous spectrum. An application to the restriction pi/(H) Of discrete series pi for a symmetric space G/H is also given.