Branching laws for square integrable representations

DUFLO, M., VARGAS, J.

PROCEEDINGS OF THE JAPAN ACADEMY. SERIES A

JAPAN ACAD

Lugar: Tokio; Año: 2010 vol. 86 p. 49 - 54

0386-2194

In this note, we  study   irreducible square integrablerepresentation of a reductive Lie group with admissiblerestriction to some reductive subgroup.  We give a simple conditionwhich insures admissible restriction and that the multiplicitiesoccurring in the decomposition in irreducible representations canbe computed in a simple explicit manner by means of a linearcombination of partition functions  generalizing the multiplicityformulas due to Kostant-Heckman orHecht-Schmid. We consider also the semi-classical analogue ofthese results for coadjoint orbits.