Linearization of Poisson actions and singular values of matrix products
Symplectic Geometry
2011-11-10 v1 Representation Theory
Abstract
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.
Cite
@article{arxiv.math/0012112,
title = {Linearization of Poisson actions and singular values of matrix products},
author = {Anton Alekseev and Eckhard Meinrenken and Chris Woodward},
journal= {arXiv preprint arXiv:math/0012112},
year = {2011}
}
Comments
20 pages