Witten multiple zeta values attached to sl(4)

TL;DR

This paper proves that Witten multiple zeta values associated with sl(4) can be expressed as finite rational linear combinations of multiple zeta values of the same weight and low depth, with specific exceptions.

Contribution

It establishes a comprehensive reduction of Witten multiple zeta values for sl(4) to classical multiple zeta values, identifying exceptions involving irregular cases.

Findings

Witten multiple zeta values of weight w>3 are reducible to MZVs of depth ≤3

Nine irregular cases require additional zeta values of lower weight and depth

The results unify the understanding of Witten zeta values attached to sl(4)

Abstract

In this paper we shall prove that every Witten multiple zeta value of weight w>3 attached to sl(4) at nonnegative integer arguments is a finite rational linear combinations of MZVs of the weight w and the depths three or less, except for the nine irregular cases where the Riemann zeta value zeta(w-2) and the double zeta values of weight w-1 and depth <3 are also needed.