Jackson Integral Representations for Solutions to the Quantized Knizhnik-Zamolodchikov Equation

Abstract

The quantized Knizhnik-Zamolodchikov equations associated with the trigonometric R-matrix or the rational R-matrix of the A-type are considered. Jackson integral representations for solutions of these equations are described. Asymptotic solutions for a holonomic system of difference equations are constructed. Relations between the integral representations and the Bethe ansatz are indicated.

50 pages. (Misprints are corrected.)

Cited by in corpus (32)

• Geometry of q-Hypergeometric Functions as a Bridge between Yangians and Quantum Affine Algebras
• BPS/CFT correspondence IV: sigma models and defects in gauge theory
• Bethe vectors of GL(3)-invariant integrable models
• Current presentation for the double super-Yangian $DY(\mathfrak{gl}(m|n))$ and Bethe vectors
• Scalar products of Bethe vectors in the models with $\mathfrak{gl}(m|n)$ symmetry
• Three-Dimensional Mirror Self-Symmetry of the Cotangent Bundle of the Full Flag Variety
• GL(3)-Based Quantum Integrable Composite Models. I. Bethe Vectors
• Form factors of local operators in a one-dimensional two-component Bose gas
• Zero modes method and form factors in quantum integrable models
• Norm of Bethe vectors in models with $\mathfrak{gl}(m|n)$ symmetry
• Exact finite size groundstate of the O(n=1) loop model with open boundaries
• Scalar products in models with GL(3) trigonometric R-matrix. Highest coefficient
• Nested algebraic Bethe ansatz for deformed orthogonal and symplectic spin chains
• Bethe vectors for orthogonal integrable models
• New quiver-like varieties and Lie superalgebras
• Partial flag varieties, stable envelopes and weight functions
• QKZ-Ruijsenaars correspondence revisited
• Supersymmetric extension of qKZ-Ruijsenaars correspondence
• Bow varieties---geometry, combinatorics, characteristic classes
• Integral solutions to boundary quantum Knizhnik-Zamolodchikov equations
• Landau-Ginzburg mirror, quantum differential equations and qKZ difference equations for a partial flag variety
• Bethe Vectors for Composite Models with $\mathfrak{gl}(2|1)$ and $\mathfrak{gl}(1|2)$ Supersymmetry
• Quantum Knizhnik--Zamolodchikov equation for $U_q(\widehat{s{l}_n})$ and integral formula
• The integral formula for the solutions of the quantum Knizhnik-Zamolodchikov equation associated with $U_q({\widehat{sl}}_n)$ for |q|=1
• Solutions to the Quantized Knizhnik-Zamolodchikov Equation and the Bethe Ansatz
• Scalar products and norm of Bethe vectors in ${\mathfrak{o}}_{2n+1}$ invariant integrable models
• Free Field Approach to Solutions of the Quantum Knizhnik-Zamolodchikov Equations
• Finite size lattice results for the two-boundary Temperley--Lieb loop model
• Harmonic Analysis in d-dimensional Superconformal Field Theory
• Laurent polynomial solutions of the boundary quantum Knizhnik--Zamolodchikov equation
• One-dimensional two-component Bose gas and the algebraic Bethe ansatz
• $q$-Hypergeometric solutions of quantum differential equations, quantum Pieri rules, and Gamma theorem