On the Kostant multiplicity formula

V. Guillemin, E. Lerman, S. Sternberg

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)721-750
Number of pages30
JournalJournal of Geometry and Physics
Issue number4
StatePublished - 1988
Externally publishedYes


  • Duistermaat-Heckman polynomial
  • Hamiltonian action
  • Partition function

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Geometry and Topology


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