### 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.

Original language | English (US) |
---|---|

Pages (from-to) | 114-158 |

Number of pages | 45 |

Journal | Canadian Journal of Mathematics |

Volume | 57 |

Issue number | 1 |

State | Published - Feb 2005 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Canadian Journal of Mathematics*,

*57*(1), 114-158.

**Bending flows for sums of rank one matrices.** / Flaschka, Hermann; Millson, John.

Research output: Contribution to journal › Article

*Canadian Journal of Mathematics*, vol. 57, no. 1, pp. 114-158.

}

TY - JOUR

T1 - Bending flows for sums of rank one matrices

AU - Flaschka, Hermann

AU - Millson, John

PY - 2005/2

Y1 - 2005/2

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=14544289016&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=14544289016&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:14544289016

VL - 57

SP - 114

EP - 158

JO - Canadian Journal of Mathematics

JF - Canadian Journal of Mathematics

SN - 0008-414X

IS - 1

ER -