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Discrete Decomposability of the Restriction of A q (λ) with Respect to Reductive Subgroups II: Micro-Local Analysis and Asymptotic K-Support

Toshiyuki Kobayashi
Annals of Mathematics
Second Series, Vol. 147, No. 3 (May, 1998), pp. 709-729
Published by: Annals of Mathematics
DOI: 10.2307/120963
Stable URL: http://www.jstor.org/stable/120963
Page Count: 21
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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.
Discrete Decomposability of the Restriction of A
          q
          (λ) with Respect to Reductive Subgroups II: Micro-Local Analysis and Asymptotic K-Support
Preview not available

Abstract

Let G$^{\prime}\subset $ G be real reductive Lie groups. This paper offers a criterion on the triplet (G, G′, π ) that the irreducible unitary representation π of G splits into a discrete sum of irreducible unitary representations of a subgroup G′ when restricted to G′, each of finite multiplicity. Furthermore, we shall give an upper estimate of the multiplicity of an irreducible unitary representation of G′ occurring in π|G′.

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