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Bending Flows for Sums of Rank One Matrices

Published:2005-02-01
Printed: Feb 2005
• Hermann Flaschka
• John Millson
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Abstract

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.
 MSC Classifications: 53D20 - Momentum maps; symplectic reduction