### 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.

**An application of the reduction method to Sutherland type many-body systems.** / Fehér, L.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Geometric Methods in Physics - 31st Workshop, 2012.*vol. 61, Trends in Mathematics, vol. 61, Springer International Publishing, pp. 109-117, 31st Workshop on Geometric Methods in Physics, WGMP 2012, Bialowieza, Poland, 6/24/12.

}

TY - GEN

T1 - An application of the reduction method to Sutherland type many-body systems

AU - Fehér, L.

PY - 2013

Y1 - 2013

N2 - 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 BCn Sutherland system built on 3 arbitrary couplings for m

AB - 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 BCn Sutherland system built on 3 arbitrary couplings for m

KW - Hamiltonian reduction

KW - Integrable many-body systems

UR - http://www.scopus.com/inward/record.url?scp=84975705443&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84975705443&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9783034806442

VL - 61

T3 - Trends in Mathematics

SP - 109

EP - 117

BT - Geometric Methods in Physics - 31st Workshop, 2012

PB - Springer International Publishing

ER -