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We prove that the linearization functor from the category of Hamiltonian -actions with
group-valued moment maps in the sense of Lu, to the category of ordinary Hamiltonian -
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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