Michel DUFLO
Centre de Mathematiques de Jussieu - Universitè Paris 7 Denis Diderot
Branching rules for discrete series of Lie groups and moment maps.

Abstract: I consider a discrete series representation T of a connected real Lie group G and a closed connected subgroup H of G. I give a large class of examples (mostly for reductive G) where the restriction of T to H is a direct sum of irreducible representations of H occuring with finite multiplicities, and for which there is a formula for these multiplicities in term of partition functions. Associated to T there is a coadjoint orbit M of G. I will show how these results are related to properties of the Hamiltonian action of H in M.