Bending Flows for Sums of Rank One Matrices

http://dx.doi.org/10.4153/CJM-2005-006-3
Canad. J. Math. 57(2005), 114-158

  Published:2005-02-01
 Printed: Feb 2005

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.