On trigonometric intertwining vectors and non-dynamical \(R\)-matrix for the Ruijsenaars model

DOI10.1016/S0550-3213(97)00520-8zbMath0933.82017arXivhep-th/9704074OpenAlexW2005249368MaRDI QIDQ1367568

Bernhard Rupp

Publication date: 24 September 1997

Published in: Nuclear Physics. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9704074

zbMATH Keywords

Ruijsenaars modelBelavin \(R\)-matrixfactorized \(L\)-operatorsquantum Lax operatortrigonometric degenerationsvertex face correspondence

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Exactly solvable models; Bethe ansatz (82B23) Many-body theory; quantum Hall effect (81V70)

Related Items (23)

Planck constant as spectral parameter in integrable systems and KZB equations ⋮ Spectral duality in elliptic systems, six-dimensional gauge theories and topological strings ⋮ Anisotropic spin generalization of elliptic Macdonald-Ruijsenaars operators and \(R\)-matrix identities ⋮ ON THE INTEGRABILITY OF CLASSICAL RUIJSENAARS–SCHNEIDER MODEL OF BC₂ TYPE ⋮ Asymmetric six-vertex model and the classical Ruijsenaars-Schneider system of particles ⋮ The nondynamical \(r\)-matrix for the Ruijsenaars-Schneider model and the classical Sklyanin algebra. ⋮ Universal \(R\)-matrix for the rational seven-vertex model ⋮ Higher-order analogues of the unitarity condition for quantum \(R\)-matrices ⋮ Trigonometric integrable tops from solutions of associative Yang-Baxter equation ⋮ Hilbert space theory for reflectionless relativistic potentials ⋮ Field theory generalizations of two-body Calogero-Moser models in the form of Landau-Lifshitz equations ⋮ On R-matrix valued Lax pairs for Calogero–Moser models ⋮ Generalized model of interacting integrable tops ⋮ Systems of \(sl(2,\mathbb C)\) tops as two-particle systems ⋮ On factorized Lax pairs for classical many-body integrable systems ⋮ Associative Yang-Baxter equation for quantum (semi-)dynamical R-matrices ⋮ Quantum trace formulae for the integrals of the hyperbolic Ruijsenaars-Schneider model ⋮ Integrable \(sl(N,\mathbb C)\) tops as Calogero-Moser systems ⋮ SYMMETRIES RELATED TO YANG–BAXTER EQUATION AND REFLECTION EQUATIONS ⋮ Double-elliptic dynamical systems from generalized Mukai-Sklyanin algebras ⋮ Field analogue of the Ruijsenaars-Schneider model ⋮ Trigonometric version of quantum-classical duality in integrable systems ⋮ Nonstandard representations of type \(C\) affine Hecke algebra from \(K\)-operators.

Cites Work

• The sine-Gordon solitons as an \(N\)-body problem
• The quantum group structure associated with non-linearly extended Virasoro algebras
• Complete integrability of relativistic Calogero-Moser systems and elliptic function identities
• Universal exchange algebra for Bloch waves and Liouville theory
• Reaction-diffusion processes, critical dynamics, and quantum chains
• Ruijsenaars' commuting difference operators as commuting transfer matrices
• Quantum dynamical R-matrices and quantum Frobenius group
• New rational solutions of Yang-Baxter equation and deformed Yangians
• Dynamical symmetry of integrable quantum systems
• \((Z_ N\times\;)^{n-1}\) generalization of the chiral Potts model
• The Gervais-Neveu-Felder equation and the quantum Calogero-Moser systems
• Partition function of the eight-vertex lattice model
• YANG-BAXTER EQUATION FOR BROKEN $\mathbb{Z}_N^{\otimes n-1}$ MODELS
• Intertwining vectors and the connection between critical vertex and SOS models
• Crossing symmetry in elliptic solutions of the Yang-Baxter equation and a new L-operator for Belavin's solution
• Degenerations of Sklyanin algebra and Askey-Wilson polynomials
• Solutions of the classical Yang-Baxter equation for simple Lie algebras

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