scientific article; zbMATH DE number 1383919

zbMath0941.35089arXivq-alg/9712002MaRDI QIDQ4719396

Atsushi Nakayashiki, Vitaly O. Tarasov, Stanislav Pakuliak

Publication date: 30 January 2000

Full work available at URL: https://arxiv.org/abs/q-alg/9712002

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

zbMATH Keywords

integral formulae for solutions of the qKZ equationsquantum Knizhnik-Zamolodchikov difference equations at level zerorational solutions of the Yang-Baxter equations

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Model quantum field theories (81T10) KdV equations (Korteweg-de Vries equations) (35Q53) Vertex operators; vertex operator algebras and related structures (17B69) Applications of Lie (super)algebras to physics, etc. (17B81) Difference operators (39A70) Moduli and deformations for ordinary differential equations (e.g., Knizhnik-Zamolodchikov equation) (32G34)

Related Items

A functional model for the tensor product of level \(1\) highest and level \(-1\) lowest modules for the quantum affine algebra \(U_q(\widetilde{\mathfrak{sl}}_2)\) ⋮ Construction of determinants for the six-vertex model with domain wall boundary conditions ⋮ Replica-deformation of the SU(2)-invariant Thirring model via solutions of the qKZ equation. ⋮ Exact form factors in integrable quantum field theories: The sine-Gordon model. II ⋮ Exact form factors in integrable quantum field theories: The sine-Gordon model ⋮ Determinant formula for solutions of the quantum Knizhnik-Zamolodchikov equation associated with \(U_q (sl_n)\) at \(|q|=1\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A solution to quantum Knizhnik-Zamolodchikov equations and its application to eigenvalue problems of the Macdonald type
• Arrangements of hyperplanes and Lie algebra homology
• Quantum affine algebras and holonomic difference equations
• Diagonalization of the \(XXZ\) Hamiltonian by vertex operators
• Quantized Knizhnik-Zamolodchikov equations, quantum Yang-Baxter equation, and difference equations for \(q\)-hypergeometric functions
• Free field representation for massive integrable models
• Geometric \(q\)-hypergeometric functions as a bridge between Yangians and quantum affine algebras
• Traces of intertwining operators for the Yangian double
• Counting the local fields in sine-Gordon theory
• A central extension of \(DY_{\hbar}(\mathfrak{gl}_ 2)\)
• Integral and theta formulae for solutions of \(sl_N\) Knizhnik-Zamolodchikov equation at level zero
• SOME INTEGRAL FORMULAS FOR THE SOLUTIONS OF THE sl₂ dKZ EQUATION WITH LEVEL −4
• HYPERGEOMETRIC-TYPE INTEGRALS AND THE $\mathfrak{sl}(2, {\rm C})$ KNIZHNIK-ZAMOLODCHIKOV EQUATION
• DYNAMICAL SYMMETRIES OF MASSIVE INTEGRABLE MODELS 1: FORM FACTOR BOOTSTRAP EQUATIONS AS A SPECIAL CASE OF DEFORMED KNIZHNIK-ZAMOLODCHIKOV EQUATIONS
• Quantum KZ equation with |q| = 1 and correlation functions of theXXZmodel in the gapless regime
• Smirnov's integrals and the quantum Knizhnik-Zamolodchikov equation of level 0
• Quantum Knizhnik-Zamolodchikov equation for U_q(sl_n) and integral formula