Integrable System of Generalized Relativistic Interacting Tops

Abstract

A family of integrable $GL(NM)$ models is described. On the one hand it generalizes the classical spin Ruijsenaars--Schneider systems (the case $N=1$), and on the other hand it generalizes the relativistic integrable tops on $GL(N)$ Lie group (the case $M=1$). The described models are obtained by means of the Lax pair with spectral parameter. Equations of motion are derived. For the construction of the Lax representation the $GL(N)$ $R$--matrix in the fundamental representation of $GL(N)$ is used.

arXiv comment13 pages

References in corpus (15)

• Spin generalization of the Ruijsenaars-Schneider model, non-abelian 2D Toda chain and representations of Sklyanin algebra
• Relativistic Classical Integrable Tops and Quantum R-matrices
• Characteristic Classes of SL(N)-Bundles and Quantum Dynamical Elliptic R-Matrices
• Rational Top and its Classical R-matrix
• Quantum Baxter-Belavin R-matrices and multidimensional Lax pairs for Painleve VI
• R-matrix-valued Lax pairs and long-range spin chains
• Poisson-Lie analogues of spin Sutherland models
• Noncommutative extensions of elliptic integrable Euler-Arnold tops and Painleve VI equation
• Calogero-Moser models with noncommutative spin interactions
• On the Hamiltonian formulation of the trigonometric spin Ruijsenaars-Schneider system
• Generalized model of interacting integrable tops
• On Hamiltonian structure of the spin Ruijsenaars-Schneider model
• On R-matrix valued Lax pairs for Calogero-Moser models
• Spin versions of the complex trigonometric Ruijsenaars-Schneider model from cyclic quivers
• Relativistic interacting integrable elliptic tops

Cited by in corpus (4)

• Elliptic generalization of integrable q-deformed anisotropic Haldane-Shastry long-range spin chain
• Lax equations for relativistic $\mathrm{GL}(NM,\mathbb{C})$ Gaudin models on elliptic curve
• Supersymmetric generalization of q-deformed long-range spin chains of Haldane-Shastry type and trigonometric GL(N|M) solution of associative Yang-Baxter equation
• Integrable systems on multiplicative quiver varieties from cyclic quivers