### Abstract

In this work, we consider the periodic Kostant–Toda flow on matrix loops in sl(n, C) of level k, which correspond to periodic infinite band matrices with period n with lower bandwidth equal to k and fixed upper bandwidth equal to 1 with 1’s on the first superdiagonal. We show that the coadjoint orbits through the submanifold of such matrix loops can be identified with those of a finite-dimensional Lie group, which appears in the form of a semi-direct product. We then characterize the generic coadjoint orbits and obtain an explicit global cross-section for such orbits. We also establish the Liouville integrability of the periodic Kostant–Toda flow on such orbits via the construction of action-angle variables.

Original language | English (US) |
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Pages (from-to) | 1153-1203 |

Number of pages | 51 |

Journal | Communications In Mathematical Physics |

Volume | 352 |

Issue number | 3 |

DOIs | |

State | Published - Jun 1 2017 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics