Algebraic Bethe ansatz for the elliptic quantum group \(E_{\tau,\eta} (sl_2\))

DOI10.1016/S0550-3213(96)00461-0zbMath0925.17020arXivq-alg/9605024OpenAlexW2238992117MaRDI QIDQ1815532

Giovanni Felder, Alexander Varchenko

Publication date: 12 November 1996

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

Full work available at URL: https://arxiv.org/abs/q-alg/9605024

zbMATH Keywords

eigenvectorsintegrable modelsspin chainscommuting transfer matricesHermite Lame equation solutiontwo-body Ruijsenaars operator

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)

Related Items (43)

Analytic theory of the eight-vertex model ⋮ Elliptic quantum groups and Baxter relations ⋮ Representation of the boundary elliptic quantum group \(BE_{\tau,\eta}(\text{sl}_2)\) and the Bethe ansatz ⋮ Dynamical stochastic higher spin vertex models ⋮ Eigenvalues of Ruijsenaars–Schneider models associated with An−1 root system in Bethe ansatz formalism ⋮ Symmetric elliptic functions, IRF models, and dynamic exclusion processes ⋮ Baxter operators and asymptotic representations ⋮ Length-two representations of quantum affine superalgebras and Baxter operators ⋮ Algebraic Bethe ansatz for the elliptic quantum group \(E_{\tau,\eta}(sl_n)\) and its applications ⋮ Inversion identities for inhomogeneous face models ⋮ Drinfeld twists of the open XXZ chain with non-diagonal boundary terms ⋮ Determinant formula for the partition function of the six-vertex model with a non-diagonal reflecting end ⋮ Domain wall partition function of the eight-vertex model with a non-diagonal reflecting end ⋮ Free fermion six vertex model: symmetric functions and random domino tilings ⋮ Multiple integral representation for the trigonometric SOS model with domain wall boundaries ⋮ Algebraic Bethe ansatz for the elliptic quantum group Eτ,η(A2(2)) ⋮ The open XXZ spin chain in the SoV framework: scalar product of separate states ⋮ A class of partition functions associated with E τ,η gl3 by Izergin–Korepin analysis ⋮ MONODROMY OF SOLUTIONS OF THE ELLIPTIC QUANTUM KNIZHNIK–ZAMOLODCHIKOV–BERNARD DIFFERENCE EQUATIONS ⋮ The partition function of the trigonometric SOS model with a reflecting end ⋮ Spontaneous staggered polarizations of the cyclic solid-on-solid model from the algebraic Bethe Ansatz ⋮ An algebraic Bethe ansatz approach to form factors and correlation functions of the cyclic eight-vertex solid-on-solid model ⋮ Multi-point local height probabilities of the CSOS model within the algebraic Bethe ansatz framework ⋮ Elliptic free-fermion model with OS boundary and elliptic Pfaffians ⋮ Antiperiodic dynamical 6-vertex model by separation of variables II: functional equations and form factors ⋮ Dynamical spin chains in 4D \(\mathcal{N} = 2\) SCFTs ⋮ Higher spin six vertex model and symmetric rational functions ⋮ Affine Macdonald conjectures and special values of Felder-Varchenko functions ⋮ Stochasticization of solutions to the Yang-Baxter equation ⋮ Determinant representations of scalar products for the open XXZ chain with non-diagonal boundary terms ⋮ Scalar products of the open XYZ chain with non-diagonal boundary terms ⋮ SOLITONS ON NONCOMMUTATIVE TORUS AS ELLIPTIC CALOGERO–GAUDIN MODELS, BRANES AND LAUGHLIN WAVE FUNCTIONS ⋮ Quantum groups for restricted SOS models ⋮ Elliptic dynamical reflection algebra and partition function of SOS model with reflecting end ⋮ Generalized Lamé functions. I. The elliptic case ⋮ Elliptic Kac-Sylvester matrix from difference Lamé equation ⋮ Algebraic integrability of the two-body Ruijsenaars operator ⋮ Elliptic quantum groups and Ruijsenaars models ⋮ Elliptic Gaudin models and elliptic KZ equations ⋮ Universal vertex-IRF transformation for quantum affine algebras ⋮ Integral formula for elliptic SOS models with domain walls and a reflecting end ⋮ Connection problems for quantum affine KZ equations and integrable lattice models ⋮ RESONANCE RELATIONS FOR SOLUTIONS OF THE ELLIPTIC QKZB EQUATIONS, FUSION RULES, AND EIGENVECTORS OF TRANSFER MATRICES OF RESTRICTED INTERACTION-ROUND-A-FACE MODELS

Cites Work

• On representations of the elliptic quantum group \(E_ \tau,\eta(sl_ 2)\)
• Some algebraic structures connected with the Yang-Baxter equation. Representations of quantum algebras
• Eight-vertex SOS model and generalized Rogers-Ramanujan-type identities
• Complete integrability of relativistic Calogero-Moser systems and elliptic function identities
• CRITICAL RSOS MODELS AND CONFORMAL FIELD THEORY
• Eight-vertex model in lattice statistics and one-dimensional anisotropic Heisenberg chain. III: Eigenvectors of the transfer matrix and Hamiltonian.
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