Abstract
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.
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Communicated by V. Guillemin
Supported by an ONR Graduate Fellowship.
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Woodward, C. The classification of transversal multiplicity-free group actions. Ann Glob Anal Geom 14, 3–42 (1996). https://doi.org/10.1007/BF00128193
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DOI: https://doi.org/10.1007/BF00128193