Elliptic Ruijsenaars-Schneider model via the Poisson reduction of the Affine Heisenberg Double

Abstract

It is shown that the elliptic Ruijsenaars-Schneider model can be obtained from the affine Heisenberg Double by means of the Poisson reduction procedure. The dynamical $r$-matrix naturally appears in the construction.

latex, 15 pages, a new section is added where we show that the problem of solving the equations of motion is equivalent to the factorization problem

References in corpus (6)

• Hamiltonian systems of Calogero type and two dimensional Yang-Mills theory
• Relativistic Calogero-Moser model as gauged WZW theory
• Classical R-matrix structure for the Calogero model
• $R$-matrices for Elliptic Calogero-Moser Models
• Exact Yangian Symmetry in the Classical Euler-Calogero-Moser Model
• Dynamical r-matrix for the elliptic Ruijsenaars-Schneider system

Cited by in corpus (8)

• Double Elliptic Dynamical Systems From Generalized Mukai - Sklyanin Algebras
• On the Hamiltonian formulation of the trigonometric spin Ruijsenaars-Schneider system
• Multiplicative Hitchin Systems and Supersymmetric Gauge Theory
• On Hamiltonian structure of the spin Ruijsenaars-Schneider model
• Poisson-Lie generalization of the Kazhdan-Kostant-Sternberg reduction
• New Results from Glueball Superpotentials and Matrix Models: the Leigh-Strassler Deformation
• Quantum Twist-Deformed D=4 Phase Spaces with Spin Sector and Hopf Algebroid Structures
• Self-duality and scattering map for the hyperbolic van Diejen systems with two coupling parameters (with an appendix by S. Ruijsenaars)