# Automorphisms of multiplicity free Hamiltonian manifolds

@inproceedings{Knop2011AutomorphismsOM, title={Automorphisms of multiplicity free Hamiltonian manifolds}, author={Friedrich Knop}, year={2011} }

Let M be a multiplicity free Hamiltonian manifold M for a connected compact Lie group K (not necessarily abelian). Let P be the momentum polytope of M. We calculate the automorphism of M as a sheaf over P and show that all higher cohomology groups of this sheaf vanish. From this, and a recent theorem of Losev, we deduce a conjecture of Delzant: the momentum polytope and the principal isotropy group determine M up to isomorphism. Moreover, we give a criterion for when a polytope and a group are… CONTINUE READING

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