Linearization of Poisson actions and singular values of matrix products

Details Linearization of Poisson actions and singular values of matrix products Linearization of Poisson actions and singular values of matrix products

2000-12-14

arxiv.org/abs/math/0012112v1

Ann. Inst. Fourier (Grenoble) 51 (2001), no. 6, 1691--1717

Mathematics

Symplectic Geometry

20 pages

Scientific paper

We prove that the linearization functor from the category of Hamiltonian K-actions with group-valued moment maps in the sense of Lu, to the category of ordinary Hamiltonian K-actions, preserves products up to symplectic isomorphism. As an application, we give a new proof of the Thompson conjecture on singular values of matrix products and extend this result to the case of real matrices. We give a formula for the Liouville volume of these spaces and obtain from it a hyperbolic version of the Duflo isomorphism.

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