RESONANCE RELATIONS FOR SOLUTIONS OF THE ELLIPTIC QKZB EQUATIONS, FUSION RULES, AND EIGENVECTORS OF TRANSFER MATRICES OF RESTRICTED INTERACTION-ROUND-A-FACE MODELS

DOI10.1142/S0219199799000146zbMath1024.81038arXivmath/9901111OpenAlexW2082212116MaRDI QIDQ4514924

Alexander Varchenko, Giovanni Felder

Publication date: 14 November 2000

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9901111

zbMATH Keywords

transfer matrixfusion rulesresonance relationsQKZB equations

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Moduli and deformations for ordinary differential equations (e.g., Knizhnik-Zamolodchikov equation) (32G34) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)

Related Items

Framed cohomological Hall algebras and cohomological stable envelopes, Inversion identities for inhomogeneous face models, Multi-point local height probabilities of the CSOS model within the algebraic Bethe ansatz framework, Quantum groups for restricted SOS models, Traces of intertwiners for quantum groups and difference equations. I, \(q\)-deformed KZB heat equation: completeness, modular properties and \(\text{SL}(3,\mathbb Z)\).

Cites Work

• On representations of the elliptic quantum group \(E_ \tau,\eta(sl_ 2)\)
• Eight-vertex SOS model and generalized Rogers-Ramanujan-type identities
• Algebraic Bethe ansatz for the elliptic quantum group \(E_{\tau,\eta} (sl_2\))
• Spherical functions on affine Lie groups
• CRITICAL RSOS MODELS AND CONFORMAL FIELD THEORY