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Linearization of Poisson actions and singular values of matrix products

Anton AlekseevEckhard MeinrenkenChris Woodward — 2001

Annales de l’institut Fourier

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...

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