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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Automorphisms of multiplicity free Hamiltonian manifolds
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by Friedrich Knop PDF
J. Amer. Math. Soc. 24 (2011), 567-601

Abstract:

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.
References
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Additional Information
  • Friedrich Knop
  • Affiliation: Department of Mathematics, Universität Erlangen, Bismarckstrasse $1\frac {1}{2}$, D-91054 Erlangen, Germany
  • MR Author ID: 103390
  • ORCID: 0000-0002-4908-4060
  • Received by editor(s): August 18, 2010
  • Received by editor(s) in revised form: October 1, 2010
  • Published electronically: November 30, 2010
  • © Copyright 2010 by Friedrich Knop
  • Journal: J. Amer. Math. Soc. 24 (2011), 567-601
  • MSC (2010): Primary 53D20, 14L30, 14M27
  • DOI: https://doi.org/10.1090/S0894-0347-2010-00686-8
  • MathSciNet review: 2748401