### Abstract

We explain that the action-angle duality between the rational Ruijsena-ars-Schneider and hyperbolic Sutherland systems implies immediately the maximal superintegrability of these many-body systems. We also present a new direct proof of the Darboux form of the reduced symplectic structure that arises in the 'Ruijse-naars gauge' of the symplectic reduction underlying this case of action-angle duality. The same arguments apply to the BC_{n} generalization of the pertinent dual pair, which was recently studied by Pusztai developing a method utilized in our direct calculation of the reduced symplectic structure.

Original language | English |
---|---|

Pages (from-to) | 27-44 |

Number of pages | 18 |

Journal | Journal of Geometry and Symmetry in Physics |

Volume | 27 |

Issue number | SEPTEMBER |

Publication status | Published - Sep 2012 |

### Fingerprint

### ASJC Scopus subject areas

- Geometry and Topology
- Mathematical Physics

### Cite this

*Journal of Geometry and Symmetry in Physics*,

*27*(SEPTEMBER), 27-44.

**Superintegrability of rational Ruijsenaars-Schneider systems and their action-angle duals.** / Ayadi, Viktor; Fehér, L.; Görbe, Tamás F.

Research output: Contribution to journal › Article

*Journal of Geometry and Symmetry in Physics*, vol. 27, no. SEPTEMBER, pp. 27-44.

}

TY - JOUR

T1 - Superintegrability of rational Ruijsenaars-Schneider systems and their action-angle duals

AU - Ayadi, Viktor

AU - Fehér, L.

AU - Görbe, Tamás F.

PY - 2012/9

Y1 - 2012/9

N2 - We explain that the action-angle duality between the rational Ruijsena-ars-Schneider and hyperbolic Sutherland systems implies immediately the maximal superintegrability of these many-body systems. We also present a new direct proof of the Darboux form of the reduced symplectic structure that arises in the 'Ruijse-naars gauge' of the symplectic reduction underlying this case of action-angle duality. The same arguments apply to the BCn generalization of the pertinent dual pair, which was recently studied by Pusztai developing a method utilized in our direct calculation of the reduced symplectic structure.

AB - We explain that the action-angle duality between the rational Ruijsena-ars-Schneider and hyperbolic Sutherland systems implies immediately the maximal superintegrability of these many-body systems. We also present a new direct proof of the Darboux form of the reduced symplectic structure that arises in the 'Ruijse-naars gauge' of the symplectic reduction underlying this case of action-angle duality. The same arguments apply to the BCn generalization of the pertinent dual pair, which was recently studied by Pusztai developing a method utilized in our direct calculation of the reduced symplectic structure.

UR - http://www.scopus.com/inward/record.url?scp=84871297934&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84871297934&partnerID=8YFLogxK

M3 - Article

VL - 27

SP - 27

EP - 44

JO - Journal of Geometry and Symmetry in Physics

JF - Journal of Geometry and Symmetry in Physics

SN - 1312-5192

IS - SEPTEMBER

ER -