Cluster Polylogarithms I: Quadrangular Polylogarithms

Published 2 Aug 2022 in math.AG and math.NT | (2208.01564v2)

Abstract: We suggest a definition of cluster polylogarithms on an arbitrary cluster variety and classify them in type $A$. We find functional equations for multiple polylogarithms which generalize equations discovered by Abel, Kummer, and Goncharov to an arbitrary weight. As an application, we prove a part of the Goncharov depth conjecture in weight six.

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