Linearization of Poisson actions and singular values of matrix products

Anton Alekseev[1]; Eckhard Meinrenken[2]; Chris Woodward[3]

  • [1] Université de Genève, Section de Mathématiques, 2-4 rue du Lièvre, Case Postale 240, 1211 Genève 24 (Suisse)
  • [2] University of Toronto, Department of Mathematics, 100 St George Street, Toronto, Ont. (Canada)
  • [3] Rutgers University, Mathematics, Hill Center,110 Frelinghuysen road, Piscataway NJ 08854-8019 (USA )

Annales de l’institut Fourier (2001)

  • Volume: 51, Issue: 6, page 1691-1717
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Alekseev, Anton, Meinrenken, Eckhard, and Woodward, Chris. "Linearization of Poisson actions and singular values of matrix products." Annales de l’institut Fourier 51.6 (2001): 1691-1717. <http://eudml.org/doc/115964>.

@article{Alekseev2001,
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.},
affiliation = {Université de Genève, Section de Mathématiques, 2-4 rue du Lièvre, Case Postale 240, 1211 Genève 24 (Suisse); University of Toronto, Department of Mathematics, 100 St George Street, Toronto, Ont. (Canada); Rutgers University, Mathematics, Hill Center,110 Frelinghuysen road, Piscataway NJ 08854-8019 (USA )},
author = {Alekseev, Anton, Meinrenken, Eckhard, Woodward, Chris},
journal = {Annales de l’institut Fourier},
keywords = {moment maps; Poisson-Lie groups; singular values; symplectic manifold; Thomson conjecture; Duflo factor},
language = {eng},
number = {6},
pages = {1691-1717},
publisher = {Association des Annales de l'Institut Fourier},
title = {Linearization of Poisson actions and singular values of matrix products},
url = {http://eudml.org/doc/115964},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Alekseev, Anton
AU - Meinrenken, Eckhard
AU - Woodward, Chris
TI - Linearization of Poisson actions and singular values of matrix products
JO - Annales de l’institut Fourier
PY - 2001
PB - Association des Annales de l'Institut Fourier
VL - 51
IS - 6
SP - 1691
EP - 1717
AB - 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.
LA - eng
KW - moment maps; Poisson-Lie groups; singular values; symplectic manifold; Thomson conjecture; Duflo factor
UR - http://eudml.org/doc/115964
ER -

References

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