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arXiv · 1909.13869

Explicit formulas for Grassmannian polylogarithms

Steven Charlton·Herbert Gangl·Danylo Radchenko
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Abstract

We give new explicit formulas for Grassmannian and Aomoto polylogarithms in terms of iterated integrals, for arbitrary weight. We also explicitly reduce the Grassmannian polylogarithm in weight 4 and in weight 5 each to depth 2. Furthermore, using this reduction in weight 4 we obtain an explicit, albeit complicated, form of the so-called 4-ratio, which gives an expression for the Borel class in continuous cohomology of $\mathrm{GL}_4$ in terms of $\mathrm{Li}_4$.

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Steven Charlton, Herbert Gangl, Danylo Radchenko. 2019-09-30. Explicit formulas for Grassmannian polylogarithms. https://arxiv.org/abs/1909.13869

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