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Linear hamiltonian circle actions that generate minimal Hilbert bases

Ágúst Sverrir Egilsson (2000)

Annales de l'institut Fourier

The orbit space of a linear Hamiltonian circle action and the reduced orbit space, at zero, are examples of singular Poisson spaces. The orbit space inherits the Poisson algebra of functions invariant under the linear circle action and the reduced orbit space inherits the Poisson algebra obtained by restricting the invariant functions to the reduced space. Both spaces reside inside smooth manifolds, which in turn inherit almost Poisson structures from the Poisson varieties. In this paper we consider...

Linearization of Poisson actions and singular values of matrix products

Anton Alekseev, Eckhard Meinrenken, Chris 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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