2019/09/30 by Steven Charlton, Charlton, Steven, Herbert Gangl +3
Mathematics · #Advanced Mathematical Identities #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics
paper · pdf · doi:10.48550/arxiv.1909.13869
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 GL4 in terms of Li4.