Witten Multiple Zeta Values Attached to $\mathfrak{sl}(4)$

Abstract

In this paper we shall prove that every Witten multiple zeta value of weight $w>3$ attached to $\mathfrak{sl}(4)$ at nonnegative integer arguments is a finite $\mathbb{Q}$-linear combination of MZVs of weight $w$ and depth 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.