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On rational symplectic parametrization of the coadjoint orbit of $ \mathrm{GL}(N)$. Diagonalizable case

Authors: M. V. Babich and S. E. Derkachov
Translated by: the authors
Original publication: Algebra i Analiz, tom 22 (2010), nomer 3.
Journal: St. Petersburg Math. J. 22 (2011), 347-357
MSC (2010): Primary 53D05
Published electronically: March 17, 2011
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Abstract | References | Similar Articles | Additional Information

Abstract: A method for constructing birational Darboux coordinates on a coadjoint orbit of the general linear group is presented. This method is based on the Gauss decomposition of a matrix in the product of an upper-triangular and a lower-triangular matrix. The method works uniformly for the orbits formed by the diagonalizable matrices of any size and for arbitrary dimensions of the eigenspaces.

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Additional Information

M. V. Babich
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, 27 Fontanka, St. Petersburg 191023, Russia

S. E. Derkachov
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, 27 Fontanka, St. Petersburg 191023, Russia

Keywords: Darboux coordinates, symplectic form, Poisson bracket, coadjoint orbit
Received by editor(s): February 15, 2010
Published electronically: March 17, 2011
Dedicated: Dedicated to L. D. Faddeev on the occasion of his 75th birthday
Article copyright: © Copyright 2011 American Mathematical Society