The classification of transversal multiplicity-free group actions

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Multiplicity-free Hamiltonian group actions are the symplectic analogs of multiplicity-free representations, that is, representations in which each irreducible appears at most once. The most well-known examples are toric varieties. The purpose of this paper is to show that under certain assumptions multiplicity-free actions whose moment maps are transversal to a Cartan subalgebra are in one-to-one correspondence with a certain collection of convex polytopes. This result generalizes a theorem of Delzant concerning torus actions.

Original languageEnglish (US)
Pages (from-to)3-42
Number of pages40
JournalAnnals of Global Analysis and Geometry
Issue number1
StatePublished - 1996
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Political Science and International Relations
  • Geometry and Topology


  • Completely integrable actions
  • Hamiltonian actions
  • Spherical varieties


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