On the Kostant multiplicity formula

The Kostant multiplicity formula is a recipe for computing the weight multiplicities of an irreducible representation of a compact semi-simple Lie group. We describe here a generalization of Kostant's formula: Suppose τ is a Hamiltonian action of a compact Lie group on a compact symplectic manifold. For an appropriate «quantization», τ^Q, of τ the weight multiplicaties of τ^Q are given by a formula similar to Konstant's. There is also an asymptotic version of this formula which gives a recipe for computing the Duistermaat Heckman polynomials associated with τ.