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Witten multiple zeta values attached to $$\mathfrak {sl}(4)$$. (English) Zbl 1239.11100
Let $\zeta_{d}((s_{\mathbf i})_{{\mathbf i}\subseteq [d]}):=\sum_{m_{1},...,m_{d}=1}^{\infty}\prod _{{\mathbf i}\subseteq [d]}(\sum_{j=1}^{lg({\mathbf i})}m_{i_{j}})^{-s_{\mathbf i}}.$ In this paper, the authors 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.
The authors use a series of reductions to prove the result.

##### MSC:
 11M41 Other Dirichlet series and zeta functions 11M32 Multiple Dirichlet series and zeta functions and multizeta values
##### Keywords:
Witten multiple zeta function; multiple zeta values; weight
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