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We derive a Hamiltonian structure for the $N$-particle hyperbolic spin Ruijsenaars-Schneider model by means of Poisson reduction of a suitable initial phase space.
1902
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1985
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S. N. M. Ruijsenaars and H. Schneider, “A New Class of Integrable Systems and Its Relation to Solitons,” Annals Phys. 170
1986
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S. N. M. Ruijsenaars, “Complete Integrability of Relativistic Calogero-moser Systems and Elliptic Function Identities,” Commun. Math. Phys. 110
1987
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I. Krichever and A. Zabrodin, “Spin generalization of the Ruijsenaars-Schneider model, nonAbelian 2-d Toda chain and representations of Sklyanin algebra,” Russ. Math. Surveys 50
1995
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A. Gorsky and N. Nekrasov, “Relativistic Calogero-Moser model as gauged WZW theory,” Nucl. Phys. B 436
1995
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H. Flaschka and T. Ratiu. “A convexity theorem for poisson actions of compact Lie groups,” Annales scientifiques de l’École Normale Supérieure, Ser. 4
1996
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G. E. Arutyunov, S. A. Frolov and P. B. Medvedev, “Elliptic Ruijsenaars-Schneider model from the cotangent bundle over the two-dimensional current group,” J. Math. Phys. 38
1997
Cited alongside, same era.
G. E. Arutyunov, S. A. Frolov and P. B. Medvedev, “Elliptic Ruijsenaars-Schneider model via the Poisson reduction of the affine Heisenberg double,” J. Phys. A 30
1997
Cited alongside, same era.
G. E. Arutyunov and S. A. Frolov, “On Hamiltonian structure of the spin Ruijsenaars-Schneider model,” J. Phys. A 31
1998
G. E. Arutyunov, L. Chekhov and S. Frolov, “ R R -Matrix Quantization of the Elliptic Ruijsenaars-Schneider Model,” Commun. Math. Phys., 192
1998
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2009
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2011
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2016
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N. Reshetikhin, “Degenerately Integrable Systems,” J. Math. Sci. 213
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Cited alongside, same era.
G. E. Arutyunov and S. A. Frolov, “Quantum Dynamical R-matrices and Quantum Frobenius Group,” Commun. Math. Phys. 191
1998
Cited alongside, same era.
A. Gorsky and N. Nekrasov, “Elliptic Calogero-Moser system from two-dimensional current algebra,” hep-th/9401021
Cited in the paper.
L. Fehér, “Poisson-Lie analogues of spin Sutherland models,” arXiv:1809.01529 [math-ph]
Cited in the paper.
Cited in the paper.
Cited in the paper.
G. Arutyunov, Elements of classical and quantum integrable models, Springer, to appear
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2016
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2017
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