Hyperkaehler structures and infinite-dimensional Grassmannians

Details Hyperkaehler structures and infinite-dimensional Grassmannians Hyperkaehler structures and infinite-dimensional Grassmannians

2005-11-17

arxiv.org/abs/math-ph/0511056v2

Journal of Functional Analysis 243 (2007) 158-206

Physics

Mathematical Physics

The title was initially `Hyperkahler structures on the cotangent bundle of the restricted grassmannian and on a natural comple

Scientific paper

10.1016/j.jfa.2006.05.019

In this paper, we describe an example of a hyperkaehler quotient of a Banach manifold by a Banach Lie group. Although the initial manifold is not diffeomorphic to a Hilbert manifold (not even to a manifold modelled on a reflexive Banach space), the quotient space obtained is a Hilbert manifold, which can furthermore be identified either with the cotangent space of a connected component of the restricted Grassmannian or with a natural complexification of this connected component, thus proving that these two manifolds are isomorphic hyperkaehler manifolds. In addition, Kaehler potentials are computed using Kostant-Souriau's theory of prequantization.

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