Duality on symmetric multiple polylogarithms

TL;DR

This paper explores dualities among symmetric multiple polylogarithms, providing proofs for their relationships using iterated integrals, and extends known dualities from complex and finite cases to the symmetric case.

Contribution

It introduces a unified proof method for dualities across complex, finite, and symmetric multiple polylogarithms, specifically establishing the symmetric case.

Findings

Proved dualities for symmetric multiple polylogarithms using iterated integrals.

Extended known dualities from complex and finite cases to symmetric case.

Provided a unified proof approach for different types of multiple polylogarithms.

Abstract

There are three kinds of multiple polylogarithms; complex, finite and symmetric. The dualities for the complex and finite cases are known. In this paper, we present proofs of them via iterated integrals and its symmetric counterpart by a similar method.