## Journal of Geometry and Symmetry in Physics

### Superintegrability of Rational Ruijsenaars-Schneider Systems and Their Action-Angle Duals

#### Abstract

We explain that the action-angle duality between the rational Ruijsenaars-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 `Ruijsenaars 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.

#### Article information

Source
J. Geom. Symmetry Phys., Volume 27 (2012), 27-44.

Dates
First available in Project Euclid: 26 May 2017

https://projecteuclid.org/euclid.jgsp/1495764126

Digital Object Identifier
doi:10.7546/jgsp-27-2012-27-44

Mathematical Reviews number (MathSciNet)
MR3026385

Zentralblatt MATH identifier
1273.81116

#### Citation

Ayadi, Viktor; Fehér, László; Görbe, Tamás F. Superintegrability of Rational Ruijsenaars-Schneider Systems and Their Action-Angle Duals. J. Geom. Symmetry Phys. 27 (2012), 27--44. doi:10.7546/jgsp-27-2012-27-44. https://projecteuclid.org/euclid.jgsp/1495764126