Explicit Rational Solution of the KZ Equation (example)

TL;DR

This paper explicitly constructs rational solutions for the Knizhnik-Zamolodchikov (KZ) system when parameters are set to specific values, advancing understanding of its solution structure.

Contribution

It provides an explicit rational solution to the KZ system for the case k=2 and n=3, building on previous proofs of rationality.

Findings

Explicit rational solution constructed for KZ system at specific parameters

Confirmed rationality of solutions for k=2, n=3 cases

Enhanced understanding of the solution structure of the KZ equations

Abstract

We investigate the Knizhnik-Zamolodchikov linear differential system. The coefficients of this system are rational functions. We have proved that the solution of the KZ system is rational when k is equal to two and n is equal to three (see [5]) . In this paper, we construct the corresponding solution in the explicit form.