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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», τQ, of τ the weight multiplicaties of τQ 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.

@article{guillemin_kostant_1988, title = {On the {Kostant} multiplicity formula}, volume = {5}, issn = {0393-0440}, url = {http://www.sciencedirect.com/science/article/pii/0393044088900265}, doi = {10.1016/0393-0440(88)90026-5}, abstract = {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», τQ, of τ the weight multiplicaties of τQ 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.}, number = {4}, urldate = {2019-09-07}, journal = {Journal of Geometry and Physics}, author = {Guillemin, V. and Lerman, E. and Sternberg, S.}, month = jan, year = {1988}, keywords = {Duistermaat-Heckman polynomial, Hamiltonian action, Partition function}, pages = {721--750} }

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