Why is the Ruijsenaars-Schneider hierarchy governed by the same \(R\)-operator as the Calogero-Moser one?

DOI10.1016/S0375-9601(96)00897-3zbMath0962.81531arXivhep-th/9602160MaRDI QIDQ1968132

Yuri Borisovich Suris

Publication date: 7 March 2000

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9602160

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Many-body theory; quantum Hall effect (81V70)

Related Items (13)

The nondynamical \(r\)-matrix for the Ruijsenaars-Schneider model and the classical Sklyanin algebra. ⋮ On the Hamiltonian formulation of the trigonometric spin Ruijsenaars-Schneider system ⋮ Integrability of the Cn and BCn Ruijsenaars–Schneider models ⋮ Integrable discretizations of the spin Ruijsenaars–Schneider models ⋮ The dynamical twisting and nondynamical r-matrix structure of the elliptic Ruijsenaars–Schneider model ⋮ Reduction of a bi-Hamiltonian hierarchy on \(T^\ast\text{U}(n)\) to spin Ruijsenaars-Sutherland models ⋮ Hilbert space theory for reflectionless relativistic potentials ⋮ The Lax pairs for elliptic Cn and BCn Ruijsenaars–Schneider models and their spectral curves ⋮ From Hamiltonian to zero curvature formulation for classical integrable boundary conditions ⋮ On the classical \(r\)-matrix structure of the rational \(BC_n\) Ruijsenaars-Schneider-van Diejen system ⋮ Quantum trace formulae for the integrals of the hyperbolic Ruijsenaars-Schneider model ⋮ Explicit solutions of the classical Calogero and Sutherland systems for any root system ⋮ On the r-matrix structure of the hyperbolic BC n Sutherland model

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