### Abstract

We study Hamiltonian reductions of the free geodesic motion on a non-compact simple Lie group using as reduction group the direct product of a maximal compact subgroup and the fixed point subgroup of an arbitrary involution commuting with the Cartan involution. In general, we describe the reduced system that arises upon restriction to a dense open submanifold and interpret it as a spin Sutherland system. This dense open part yields the full reduced system in important special examples without spin degrees of freedom, which include the BC_{n} Sutherland system built on 3 arbitrary couplings for m <n positively charged and (n-m) negatively charged particles moving on the half-line.

Original language | English |
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Title of host publication | Geometric Methods in Physics - 31st Workshop, 2012 |

Publisher | Springer International Publishing |

Pages | 109-117 |

Number of pages | 9 |

Volume | 61 |

ISBN (Print) | 9783034806442 |

Publication status | Published - 2013 |

Event | 31st Workshop on Geometric Methods in Physics, WGMP 2012 - Bialowieza, Poland Duration: Jun 24 2012 → Jun 30 2012 |

### Publication series

Name | Trends in Mathematics |
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Volume | 61 |

ISSN (Print) | 22970215 |

ISSN (Electronic) | 2297024X |

### Other

Other | 31st Workshop on Geometric Methods in Physics, WGMP 2012 |
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Country | Poland |

City | Bialowieza |

Period | 6/24/12 → 6/30/12 |

### Fingerprint

### Keywords

- Hamiltonian reduction
- Integrable many-body systems

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Geometric Methods in Physics - 31st Workshop, 2012*(Vol. 61, pp. 109-117). (Trends in Mathematics; Vol. 61). Springer International Publishing.