A simple construction of Grassmannian polylogarithms

TL;DR

The paper presents a straightforward explicit method to construct Grassmannian n-logarithms, exploring Tate iterated integrals and introducing a Hopf algebra framework to understand these complex functions.

Contribution

It provides a new simple explicit formula for Grassmannian polylogarithms and introduces a Hopf algebra of integrable symbols for algebraic varieties.

Findings

Explicit construction of Grassmannian n-logarithms

Introduction of Hopf algebra of integrable symbols

Simple formula for Tate iterated integrals related to polylogarithms

Abstract

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.