Poisson-Lie interpretation of trigonometric Ruijsenaars duality

Details Poisson-Lie interpretation of trigonometric Ruijsenaars duality Poisson-Lie interpretation of trigonometric Ruijsenaars duality

2009-06-23

arxiv.org/abs/0906.4198v3

Commun.Math.Phys.301:55-104,2011

Physics

Mathematical Physics

modified Theorem 3.1 and added new results in v2, 49 pages; v3: final version (with a reference added) to appear in CMP

Scientific paper

10.1007/s00220-010-1140-6

A geometric interpretation of the duality between two real forms of the complex trigonometric Ruijsenaars-Schneider system is presented. The phase spaces of the systems in duality are viewed as two different models of the same reduced phase space arising from a suitable symplectic reduction of the standard Heisenberg double of U(n). The collections of commuting Hamiltonians of the systems in duality are shown to descend from two families of `free' Hamiltonians on the double which are dual to each other in a Poisson-Lie sense. Our results give rise to a major simplification of Ruijsenaars' proof of the crucial symplectomorphism property of the duality map.

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