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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
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