A simple construction of Grassmannian polylogarithms

Details A simple construction of Grassmannian polylogarithms A simple construction of Grassmannian polylogarithms

2009-08-16

arxiv.org/abs/0908.2238v3

Mathematics

Algebraic Geometry

25 pages. Dedicated to A.Suslin's 60th birthday

Scientific paper

We give a simple explicit construction of the Grassmannian n-logarithm, which is a multivalued analytic function on the quotient of the Grassmannian of generic n-dimensional subspaces in 2n-dimensional coordinate complex vector space by the action of the 2n-dimensional coordinate torus. We study Tate iterated integrals, which are homotopy invariant integrals of 1-forms dlog(rational functions). We introduce the Hopf algebra of integrable symbols related to an algebraic variety, which controls the Tate iterated integrals We give a simple explicit formula for the Tate iterated integrals related to the Grassmannian polylogarithms.

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