The Ruijsenaars self-duality map as a mapping class symplectomorphism

L. Fehér, C. Klimčík

Research output: Contribution to journalArticle

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Abstract

This is a brief review of the main results of our paper [Nucl. Phys. B 860, 464-515 (2012)] 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.

Original languageEnglish
Pages (from-to)423-437
Number of pages15
JournalUnknown Journal
Volume36
DOIs
Publication statusPublished - 2013

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Duality Maps
Self-duality
Phase Space
Moment Map
Symplectic Form
Complex Projective Space
Open Problems
Torus
Generator
Class

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

The Ruijsenaars self-duality map as a mapping class symplectomorphism. / Fehér, L.; Klimčík, C.

In: Unknown Journal, Vol. 36, 2013, p. 423-437.

Research output: Contribution to journalArticle

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