Motivic Multiple Zeta Values and the Block Filtration

TL;DR

This paper extends the block filtration to all motivic multiple zeta values, constructs a Lie algebra for their relations, and proves several conjectures and new symmetries within this framework.

Contribution

It introduces a comprehensive extension of the block filtration to all motivic multiple zeta values and proves key conjectures and symmetries in this structure.

Findings

Proved Charlton's cyclic insertion conjecture.

Discovered a new dihedral symmetry.

Established the existence of a block shuffle relation.

Abstract

We extend the block filtration, defined by Brown based on the work of Charlton, to all motivic multiple zeta values, and study relations compatible with this filtration. We construct a Lie algebra describing relations among motivic multiple zeta values modulo terms of lower block degree, proving Charlton's cyclic insertion conjecture in this structure, and showing the existence of a `block shuffle' relation, and a previously unknown dihedral symmetry and differential relation.