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arXiv · 1203.3300

The Ruijsenaars self-duality map as a mapping class symplectomorphism

L. Feher·C. Klimcik
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Abstract

This is a brief review of the main results of our paper arXiv:1101.1759 that contains a complete global treatment of the compactified trigonometric Ruijsenaars-Schneider system by quasi-Hamiltonian reduction. Confirming previous conjectures of Gorsky and collaborators, we have rigorously established the interpretation of the system in terms of flat SU(n) connections on the one-holed torus and demonstrated that its self-duality symplectomorphism represents the natural action of the standard mapping class generator S on the phase space. The pertinent quasi-Hamiltonian reduced phase space turned out to be symplectomorphic to the complex projective space equipped with a multiple of the Fubini-Study symplectic form and two toric moment maps playing the roles of particle-positions and action-variables that are exchanged by the duality map. Open problems and possible directions for future work are also discussed.

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L. Feher, C. Klimcik. 2012-03-15. The Ruijsenaars self-duality map as a mapping class symplectomorphism. https://arxiv.org/abs/1203.3300

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