Open Access
2012 Superintegrability of Rational Ruijsenaars-Schneider Systems and Their Action-Angle Duals
Viktor Ayadi, László Fehér, Tamás F. Görbe
J. Geom. Symmetry Phys. 27: 27-44 (2012). DOI: 10.7546/jgsp-27-2012-27-44


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.


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Viktor Ayadi. László Fehér. Tamás F. Görbe. "Superintegrability of Rational Ruijsenaars-Schneider Systems and Their Action-Angle Duals." J. Geom. Symmetry Phys. 27 27 - 44, 2012.


Published: 2012
First available in Project Euclid: 26 May 2017

zbMATH: 1273.81116
MathSciNet: MR3026385
Digital Object Identifier: 10.7546/jgsp-27-2012-27-44

Rights: Copyright © 2012 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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