The dynamical twisting and nondynamical r-matrix structure of the elliptic Ruijsenaars–Schneider model

DOI10.1063/1.533136zbMath1006.37041arXivmath/9802104OpenAlexW3123077512MaRDI QIDQ2737825

Wen-Li Yang, Bo-Yu Hou

Publication date: 30 August 2001

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9802104

zbMATH Keywords

Lax representationCalogero-Moser modelclassical \(r\)-matrixRuijsenaars-Schneider modelquadratic Poisson-Lie bracket

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Groups and algebras in quantum theory and relations with integrable systems (81R12)

Related Items (6)

Structures in BCN Ruijsenaars–Schneider models ⋮ Eigenvalues of Ruijsenaars–Schneider models associated with An−1 root system in Bethe ansatz formalism ⋮ Algebraic Bethe ansatz for the elliptic quantum group \(E_{\tau,\eta}(sl_n)\) and its applications ⋮ ON THE INTEGRABILITY OF CLASSICAL RUIJSENAARS–SCHNEIDER MODEL OF BC₂ TYPE ⋮ On the classical \(r\)-matrix structure of the rational \(BC_n\) Ruijsenaars-Schneider-van Diejen system ⋮ On the r-matrix structure of the hyperbolic BC n Sutherland model

Cites Work

• The sine-Gordon solitons as an \(N\)-body problem
• A new class of integrable systems and its relation to solitons
• Complete integrability of relativistic Calogero-Moser systems and elliptic function identities
• Elliptic solutions of the Kadomtsev-Petviashvili equation and integrable systems of particles
• Three integrable Hamiltonian systems connected with isospectral deformations
• Relativistic Calogero-Moser model as gauged WZW theory.
• Integrable time-discretization of the Ruijsenaars-Schneider model
• The Gervais-Neveu-Felder equation and the quantum Calogero-Moser systems
• Why is the Ruijsenaars-Schneider hierarchy governed by the same \(R\)-operator as the Calogero-Moser one?
• YANG-BAXTER EQUATION FOR BROKEN $\mathbb{Z}_N^{\otimes n-1}$ MODELS
• Fusion for the Function Difference Representation of Zn Sklyanin Algebra
• Algebras connected with the Z n elliptic solution of the Yang–Baxter equation
• The non-dynamicalr-matrix structure for the elliptic Calogero-Moser model
• Cyclic representation and function difference representation of the Z_nSklyanin algebra
• L-operator for Belavin’s R-matrix acting on the space of theta functions

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