Automorphisms of multiplicity free Hamiltonian manifolds

Knop, Friedrich¹

¹ Department of Mathematics, Universität Erlangen, Bismarckstrasse $1\frac{1}2$, D-91054 Erlangen, Germany

Journal of the American Mathematical Society, Tome 24 (2011) no. 2, pp. 567-601

Résumé

Let $M$ be a multiplicity free Hamiltonian manifold $M$ for a connected compact Lie group $K$ (not necessarily abelian). Let $\mathcal {P}$ be the momentum polytope of $M$. We calculate the automorphism of $M$ as a sheaf over $\mathcal {P}$ 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 afforded by a multiplicity free manifold.

Détail

DOI : 10.1090/S0894-0347-2010-00686-8

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