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DISCRETE DECOMPOSABLE BRANCHING LAWS AND PROPER MOMENTUM MAPS

SALMA NASRIN

Department of Mathematics, University of Dhaka, Dhaka-1000, Bangladesh

https://doi.org/10.1142/S0129167X11007628Cited by:2 (Source: Crossref)

Abstract

Suppose an irreducible unitary representation π of a Lie group G is obtained as a geometric quantization of a coadjoint orbit in the Kirillov–Kostant–Duflo orbit philosophy. Let H be a closed subgroup of G, and we compare the following two conditions.

(1) The restriction π|_H is discretely decomposable in the sense of Kobayashi.

(2) The momentum map is proper.

In this article, we prove that (1) is equivalent to (2) when π is any holomorphic discrete series representation of scalar type of a semisimple Lie group G and (G, H) is any symmetric pair.

Keywords:

AMSC: 22E46, 22E60, 32M15, 53C35, 81S10

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