Automorphisms of multiplicity free Hamiltonian manifolds

Abstract

We compute the sheaf of automorphisms of a multiplicity free Hamiltonian manifold over its momentum polytope and show that its higher cohomology groups vanish. Together with a theorem of Losev, arXiv:math/0612561, this implies a conjecture of Delzant: a compact multiplicity free Hamiltonian manifold is uniquely determined by its momentum polytope and its principal isotropy group.

v1: 42 pages; v2: 42 pages, abstract added, minor changes; v3: 43 pages, Corollary 11.4 added, minor changes

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