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Every symplectic manifold is a (linear) coadjoint orbit

Part of: Symplectic geometry, contact geometry Infinite-dimensional manifolds

Published online by Cambridge University Press:  18 May 2021

Paul Donato  and
Patrick Iglesias-Zemmour
Paul Donato
Affiliation:
Institut de Mathématiques de Marseille, Aix-Marseille Université, 3 Place Victor-Hugo, 13331Marseille Cedex 3, France e-mail: paul.donato@univ-amu.fr
Patrick Iglesias-Zemmour
Affiliation:
Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, 9190401Jerusalem, Israel e-mail: piz@math.huji.ac.ilURL:http://math.huji.ac.il/~piz
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Abstract

We prove that every symplectic manifold is a coadjoint orbit of the group of automorphisms of its integration bundle, acting linearly on its space of momenta, for any group of periods of the symplectic form. This result generalizes the Kirilov–Kostant–Souriau theorem when the symplectic manifold is homogeneous under the action of a Lie group and the symplectic form is integral.

Keywords

Diffeologysymplectic geometryquantization

MSC classification

Primary: 53D05: Symplectic manifolds, general
Secondary: 58B99: None of the above, but in this section
Type
Article
Information
Canadian Mathematical Bulletin , Volume 65 , Issue 2 , June 2022 , pp. 345 - 360
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Copyright
© Canadian Mathematical Society 2021

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