Branching laws for square integrable representations - Duflo, Michel (2010)
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.