KZ equation on the moduli space ${\mathcal M}_{0,5}$ and the harmonic product of multiple polylogarithms

TL;DR

This paper explores the functional relations of hyperlogarithms on the moduli space ${\mathcal M}_{0,5}$, revealing how these relations encompass the harmonic product of multiple polylogarithms and connect to the KZ equation.

Contribution

It introduces generalized harmonic product relations for hyperlogarithms on ${\mathcal M}_{0,5}$ and links them to fundamental solutions of the KZ equation.

Findings

Generalized harmonic product relations include the harmonic product of multiple polylogarithms.

Relations are equivalent to decompositions of the fundamental solution of the KZ equation.

Provides a new perspective on the structure of hyperlogarithms on moduli spaces.

Abstract

In this article, we derive a system of functional relations called the generalized harmonic product relations for hyperlogarithms on the moduli space ${\mathcal M}_{0,5}$ and show that the relations contain the harmonic product of multiple polylogarithms. The generalized harmonic product relations are equivalent to the relations which come from two decompositions of the fundamental solution normalized at the origin of the KZ equation on ${\mathcal M}_{0,5}$.