The Gervais-Neveu-Felder equation and the quantum Calogero-Moser systems

DOI10.1007/BF02099449zbMath0870.17019arXivhep-th/9505091MaRDI QIDQ1924021

Jean Avan, E. Billey, O. Babelon

Publication date: 18 September 1997

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

Full work available at URL: https://arxiv.org/abs/hep-th/9505091

zbMATH Keywords

quantum \(R\)-matrixspin Calogero-Moser model

Mathematics Subject Classification ID

Related Items (34)

Degenerate integrability of quantum spin Calogero-Moser systems ⋮ Integrability of two-species partially asymmetric exclusion processes ⋮ (T*ℬ)q, q-analog of model space and the Clebsch–Gordan coefficients generating matrices ⋮ BOUNDARY K MATRICES AND THE LAX PAIR FOR ONE-DIMENSIONAL OPEN XYZ SPIN-CHAIN ⋮ Yangian-invariant field theory of matrix-vector models ⋮ Quantum dynamical coboundary equation for finite dimensional simple Lie algebras ⋮ On trigonometric intertwining vectors and non-dynamical \(R\)-matrix for the Ruijsenaars model ⋮ A quasi-Hopf algebra interpretation of quantum \(3\)-\(j\) and \(6\)-\(j\) symbols and difference equations ⋮ Spin Calogero models obtained from dynamical \(r\)-matrices and geodesic motion ⋮ Multiscale \(N=2\) SUSY field theories, integrable systems and their stringy/brane origin ⋮ A new dynamical reflection algebra and related quantum integrable systems ⋮ Elliptic algebra, Frenkel–Kac construction and root of unity limit ⋮ Algebraic Bethe ansatz for the elliptic quantum group Eτ,η(A2(2)) ⋮ Integrable discretizations of the spin Ruijsenaars–Schneider models ⋮ The dynamical twisting and nondynamical r-matrix structure of the elliptic Ruijsenaars–Schneider model ⋮ On representations of the elliptic quantum group \(E_ \tau,\eta(sl_ 2)\) ⋮ Self-duality and scattering map for the hyperbolic van Diejen systems with two coupling parameters (with an Appendix by S. Ruijsenaars) ⋮ Trigonometric integrable tops from solutions of associative Yang-Baxter equation ⋮ The chiral WZNW phase space and its Poisson-Lie groupoid ⋮ \(R\)-matrix quantization of the elliptic Ruijsenaars-Schneider model ⋮ Dynamical Yang-Baxter equation and quantum vector bundles ⋮ Generalizations of Felder's elliptic dynamical \(r\)-matrices associated with twisted loop algebras of self-dual Lie algebras ⋮ Constructing dynamical twists over a non-Abelian base. ⋮ On R-matrix valued Lax pairs for Calogero–Moser models ⋮ On the classical \(r\)-matrix structure of the rational \(BC_n\) Ruijsenaars-Schneider-van Diejen system ⋮ Adler–Kostant–Symes scheme for face and Calogero–Moser–Sutherland-type models ⋮ A one-dimensional many-body integrable model from Zn Belavin model with open boundary conditions ⋮ Hecke algebraic properties of dynamical R -matrices. Application to related quantum matrix algebras ⋮ Spin chains from dynamical quadratic algebras ⋮ Elliptic quantum groups and Ruijsenaars models ⋮ Chiral extensions of the WZNW phase space, Poisson-Lie symmetries and groupoids ⋮ Fusion of \(q\)-tensor operators: Quasi-Hopf-algebraic point of view ⋮ Triangular dynamical \(r\)-matrices and quantization ⋮ Commuting quantum traces for quadratic algebras

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