On the solutions of Knizhnik-Zamolodchikov system

TL;DR

This paper investigates the Knizhnik-Zamolodchikov system of linear differential equations with rational coefficients, proving conditions for rational solutions, providing a construction method, and analyzing asymptotics when a parameter is integer.

Contribution

It introduces a method to construct rational solutions of the KZ system and establishes conditions under which solutions are rational.

Findings

Solutions are rational under certain conditions.

A method for constructing rational solutions is provided.

Asymptotic formulas are derived for integer parameter values.

Abstract

We consider the Knizhnik-Zamolodchikov system of linear differential equations. The coefficients of this system are rational functions. We prove that under some conditions the solution of KZ system is rational too. We give the method of constructing the corresponding rational solution. We deduce the asymptotic formulas for the solution of KZ system when $\rho$ is integer.