The restricted Grassmannian, Banach Lie-Poisson spaces, and coadjoint orbits

Details The restricted Grassmannian, Banach Lie-Poisson spaces, and coadjoint orbits The restricted Grassmannian, Banach Lie-Poisson spaces, and coadjoint orbits

2006-06-14

arxiv.org/abs/math/0606327v1

Mathematics

Differential Geometry

19 pages

Scientific paper

We investigate some basic questions concerning the relationship between the restricted Grassmannian and the theory of Banach Lie-Poisson spaces. By using universal central extensions of Lie algebras, we find that the restricted Grassmannian is symplectomorphic to symplectic leaves in certain Banach Lie-Poisson spaces, and the underlying Banach space can be chosen to be even a Hilbert space. Smoothness of numerous adjoint and coadjoint orbits of the restricted unitary group is also established. Several pathological properties of the restricted algebra are pointed out.

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