Poisson-Lie generalization of the Kazhdan-Kostant-Sternberg reduction

Abstract

The trigonometric Ruijsenaars-Schneider model is derived by symplectic reduction of Poisson-Lie symmetric free motion on the group U(n). The commuting flows of the model are effortlessly obtained by reducing canonical free flows on the Heisenberg double of U(n). The free flows are associated with a very simple Lax matrix, which is shown to yield the Ruijsenaars-Schneider Lax matrix upon reduction.

arXiv comment13 pages, LaTeX, minor modifications and references added in v2

References in corpus (8)

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• Relativistic Calogero-Moser model as gauged WZW theory
• Duality in Integrable Systems and Gauge Theories
• The Quantum Dynamics of the Compactified Trigonometric Ruijsenaars-Schneider Model
• Elliptic Ruijsenaars-Schneider model from the cotangent bundle over the two-dimensional current group
• Elliptic Ruijsenaars-Schneider model via the Poisson reduction of the Affine Heisenberg Double
• Free motion on the Poisson SU(n) group
• On moment maps associated to a twisted Heisenberg double

Cited by in corpus (12)

• Poisson-Lie interpretation of trigonometric Ruijsenaars duality
• On the duality between the hyperbolic Sutherland and the rational Ruijsenaars-Schneider models
• Multiplicative quiver varieties and generalised Ruijsenaars-Schneider models
• Quantum Lax pairs via Dunkl and Cherednik operators
• Poisson-Lie analogues of spin Sutherland models
• On R-matrix valued Lax pairs for Calogero-Moser models
• On factorized Lax pairs for classical many-body integrable systems
• Spin versions of the complex trigonometric Ruijsenaars-Schneider model from cyclic quivers
• Quantum Trace Formulae for the Integrals of the Hyperbolic Ruijsenaars-Schneider model
• Reduction of a bi-Hamiltonian hierarchy on $T^{\ast }\mathrm{U}(n)$ to spin Ruijsenaars--Sutherland models
• A note on the Gauss decomposition of the elliptic Cauchy matrix
• Poisson-Lie analogues of spin Sutherland models revisited