Cluster Polylogarithms I: Quadrangular Polylogarithms
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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