Every Symplectic Manifold Is A (Linear) Coadjoint Orbit
November 19, 2019
 
In this paper, we prove that every symplectic manifold is a coadjoint orbit of the group of automorphisms of the integration bundle of the symplectic manifold, acting linearly on its space of momenta. And that, independantly of the number of generators of the periods of the symplectic form. This result generalizes the Kostant-Kirilov-Souriau theorem when the symplectic manifold is homogeneous under the action of a Lie group, and the symplectic form is integral.

Joint work with Paul Donato.



Submitted for publication.