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

TL;DR

This paper develops Jackson integral representations for solutions to the quantized Knizhnik-Zamolodchikov equations, connecting them with asymptotic solutions and the Bethe ansatz, advancing understanding of their structure.

Contribution

It introduces Jackson integral formulas for solutions of the quantized KZ equations and explores their relation to asymptotic solutions and Bethe ansatz methods.

Findings

Jackson integral representations are constructed for solutions.

Asymptotic solutions for difference equations are developed.

Relations between integral solutions and Bethe ansatz are discussed.

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.