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Bending Flows for Sums of Rank One Matrices

Published online by Cambridge University Press:  20 November 2018

Hermann Flaschka
Affiliation:
Department of Mathematics, The University of Arizona, Tucson, AZ 85721 e-mail: [email protected]
John Millson
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD 20742 e-mail: [email protected]
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Abstract

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We study certain symplectic quotients of $n$-fold products of complex projective $m$-space by the unitary group acting diagonally. After studying nonemptiness and smoothness of these quotients we construct the action-angle variables, defined on an open dense subset, of an integrable Hamiltonian system. The semiclassical quantization of this system reporduces formulas from the representation theory of the unitary group.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2005

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