Anisotropic spin generalization of elliptic Macdonald-Ruijsenaars operators and \(R\)-matrix identities

DOI10.1007/s00023-023-01316-yarXiv2201.05944OpenAlexW4367843790MaRDI QIDQ6073684

M. G. Matushko, Andrei V. Zotov

Publication date: 18 September 2023

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2201.05944

Mathematics Subject Classification ID

Spinor and twistor methods applied to problems in quantum theory (81R25) Algebraic geometry methods for problems in mechanics (70G55)

Related Items (1)

Higher-rank generalization of the 11-vertex rational \(R\)-matrix: IRF-vertex relations and the associative Yang-Baxter equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Classical Yang-Baxter equation and the \(A_\infty\)-constraint
• Quantum Baxter-Belavin \(R\)-matrices and multidimensional Lax pairs for Painlevé VI
• On the connection between the one-dimensional \(S=1/2\) Heisenberg chain and Haldane-Shastry model
• Complete integrability of relativistic Calogero-Moser systems and elliptic function identities
• Quantum affine algebras and holonomic difference equations
• Elliptic quantum groups and Ruijsenaars models
• Ruijsenaars' commuting difference operators as commuting transfer matrices
• On trigonometric intertwining vectors and non-dynamical \(R\)-matrix for the Ruijsenaars model
• Trigonometric solutions of the associative Yang-Baxter equation
• Dynamical symmetry of integrable quantum systems
• \(R\)-matrix-valued Lax pairs and long-range spin chains
• Elliptic Dunkl operators, root systems, and functional equations
• Induced representations of double affine Hecke algebras and applications
• Trigonometric integrable tops from solutions of associative Yang-Baxter equation
• Quadratic algebras based on \(SL(NM)\) elliptic quantum \(R\)-matrices
• Field analogue of the Ruijsenaars-Schneider model
• Spin-Ruijsenaars, \(\mathsf{q}\)-deformed Haldane-Shastry and Macdonald polynomials
• Poisson-Lie analogues of spin Sutherland models
• Relativistic interacting integrable elliptic tops
• Hyperbolic spin Ruijsenaars-Schneider model from Poisson reduction
• On the Hamiltonian formulation of the trigonometric spin Ruijsenaars-Schneider system
• Generalized model of interacting integrable tops
• Calogero-Moser model and \(R\)-matrix identities
• Quantum trace formulae for the integrals of the hyperbolic Ruijsenaars-Schneider model
• Quantum Lax pairs via Dunkl and Cherednik operators
• Partition function of the eight-vertex lattice model
• Level-0 structure of level-1 U_q(sl₂)-modules and Macdonald polynomials
• Massey Products on Cycles of Projective Lines and Trigonometric Solutions of the Yang–Baxter Equations
• Quantum integrability of the generalized elliptic Ruijsenaars models
• Yang-Baxter equation in long-range interacting systems
• On R-matrix valued Lax pairs for Calogero–Moser models
• A general formula for soliton form factors in the quantum sine-Gordon model
• Spin generalization of the Ruijsenaars-Schneider model, the non-Abelian 2D Toda chain, and representations of the Sklyanin algebra
• Characteristic classes of ${\rm SL}(N, {\mathbb {C}})$-bundles and quantum dynamical elliptic R-matrices
• Elliptic generalisation of integrable q-deformed anisotropic Haldane–Shastry long-range spin chain
• Elliptic Ruijsenaars Difference Operators on Bounded Partitions
• \(R\)-matrix quantization of the elliptic Ruijsenaars-Schneider model
• Solutions of the classical Yang-Baxter equation for simple Lie algebras

This page was built for publication: Anisotropic spin generalization of elliptic Macdonald-Ruijsenaars operators and \(R\)-matrix identities