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Bending Flows for Sums of Rank One Matrices

Published online by Cambridge University Press:  20 November 2018

Hermann Flaschka  and
John Millson
Hermann Flaschka
Affiliation:
Department of Mathematics, The University of Arizona, Tucson, AZ 85721 e-mail: flaschka@math.arizona.edu
John Millson
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD 20742 e-mail: jjm@math.umd.edu
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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

53D20
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 57 , Issue 1 , 01 February 2005 , pp. 114 - 158
Copyright
Copyright © Canadian Mathematical Society 2005

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