Branching laws for square integrable representations

Abstract

In this note, we study an irreducible square integrable representation of a reductive Lie group with admissible restriction to some reductive subgroup. We propose sufficient conditions for admissibility and, in this case, formulas for the multiplicity of each irreducible factor of the restriction, generalizing the multiplicity formulas due to Kostant-Heckman or Hecht-Schmid. We consider also the semi-classical analogue of these results for coadjoint orbits.