Virtual posets, shuffle algebras and associators

TL;DR

This paper introduces a novel method to generate new associators from Drinfel'd's KZ associator using poset-based generating functions, resulting in explicit families described by generalized multiple zeta values.

Contribution

It presents a new construction of associators via poset-based generating functions, expanding the understanding of associator families and their explicit descriptions.

Findings

Two analytic families of associators constructed

Both paths deform the KZ associator into the trivial associator

Associators parametrized by these paths are all distinct

Abstract

We provide a method to construct new associators out of Drinfel'd's KZ associator. We obtain two analytic families of associators whose coefficients we can describe explicitly by a generalization of multiple zeta values. The two families contain two different paths that deform the Drinfel'd KZ associator into the trivial associator 1. We show that both paths are injective, that is, all of the associators parametrized by them are different. Our construction is based on the observation that one can recover multiple polylogarithms as generating functions of order polynomials of certain formally constructed posets.