# STABILITY OF BRANCHING LAWS FOR HIGHEST WEIGHT MODULES

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## 抄録

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.

本文言語 English 1027-1050 24 Transformation Groups 19 4 https://doi.org/10.1007/s00031-014-9284-7 Published - 2014 11月 18 はい

• 代数と数論
• 幾何学とトポロジー

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