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March 2010 Branching laws for square integrable representations
Michel Duflo, Jorge Antonio Vargas
Proc. Japan Acad. Ser. A Math. Sci. 86(3): 49-54 (March 2010). DOI: 10.3792/pjaa.86.49

Abstract

In this note, we study square integrable representations of a real reductive Lie group with admissible restriction to some reductive subgroup. We give a simple condition which insures admissibility of the restriction, and which allows to compute the branching numbers in a simple explicit manner by means of partition functions, generalizing the multiplicity formulas due to Kostant-Heckman and Hecht-Schmid. We consider also the semi-classical analogue of these results for coadjoint orbits.

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Michel Duflo. Jorge Antonio Vargas. "Branching laws for square integrable representations." Proc. Japan Acad. Ser. A Math. Sci. 86 (3) 49 - 54, March 2010. https://doi.org/10.3792/pjaa.86.49

Information

Published: March 2010
First available in Project Euclid: 3 March 2010

zbMATH: 1196.22009
MathSciNet: MR2641797
Digital Object Identifier: 10.3792/pjaa.86.49

Subjects:
Primary: 22E46
Secondary: 05E15 , 17B10

Keywords: branching laws , discrete series , multiplicity formulas , square integrable representations

Rights: Copyright © 2010 The Japan Academy

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Vol.86 • No. 3 • March 2010
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