On the Kostant multiplicity formula. Guillemin, V., Lerman, E., & Sternberg, S. Journal of Geometry and Physics, 5(4):721–750, January, 1988.
On the Kostant multiplicity formula [link]Paper  doi  abstract   bibtex   
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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