Rational Solution of the KZ equation (example)

TL;DR

This paper proves that the solutions to the Knizhnik-Zamolodchikov (KZ) system are rational functions for specific parameters and provides explicit coefficients of the solution near singular points.

Contribution

It establishes the rationality of KZ system solutions for particular cases and computes expansion coefficients around singularities.

Findings

Solutions are rational when k=2 and n=3

Explicit coefficients of expansion near singular points are derived

Enhances understanding of the structure of KZ equations

Abstract

We investigate the Knizhnik-Zamolodchikov linear differential system. The coefficients of this system are rational functions. We prove that the solution of the KZ system is rational when $k$ is equal to two and $n$ is equal to three. While doing so, we found the coefficients of expansion in a neighborhood of a singular point.