  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.
