STABILITY OF BRANCHING LAWS FOR HIGHEST WEIGHT MODULES

Masatoshi Kitagawa

Research output: Contribution to journalArticle

Abstract

In this paper, we study the irreducible decomposition of a (ℂ[X];G)-module M for a quasi-affine spherical variety X of a connected reductive algebraic group G over ℂ. We show that for sufficiently large parameters, the decomposition of M with respect to G is reduced to the decomposition of the ‘fiber’ M/m(x0)M with respect to some reductive subgroup L of G. In particular, we obtain a method to compute the maximum value of multiplicities in M. Our main result is a generalization of earlier work by F. Satō in [17]. We apply this result to branching laws of holomorphic discrete series representations with respect to symmetric pairs of holomorphic type. We give a necessary and sufficient condition for multiplicity-freeness of the branching laws.

Original languageEnglish
Pages (from-to)1027-1050
Number of pages24
JournalTransformation Groups
Volume19
Issue number4
DOIs
Publication statusPublished - 2014 Nov 18

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ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

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