On the geometry and quantization of symplectic Howe pairs

Details On the geometry and quantization of symplectic Howe pairs On the geometry and quantization of symplectic Howe pairs

2009-10-05

arxiv.org/abs/0910.0701v1

Mathematics

Symplectic Geometry

17 pages

Scientific paper

We study the orbit structure and the geometric quantization of a pair of mutually commuting hamiltonian actions on a symplectic manifold. If the pair of actions fulfils a symplectic Howe condition, we show that there is a canonical correspondence between the orbit spaces of the respective moment images. Furthermore, we show that reduced spaces with respect to the action of one group are symplectomorphic to coadjoint orbits of the other group. In the Kaehler case we show that the linear representation of a pair of compact Lie groups on the geometric quantization of the manifold is then equipped with a representation-theoretic Howe duality.

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