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On webs, polylogarithms and cluster algebras
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In this text, we investigate webs which can be associated to cluster algebras from the point of view of the abelian functional equations these webs carry, focusing on the polylogarithmic ones. We introduce a general notion of webs whose rank is `As Maximal as Possible' (AMP) and show that many webs associated either to polylogarithmic functional equations or to cluster algebras are of this type. In particular, we prove a few results and state some conjectures about cluster webs associated to (pairs of) Dynkin diagrams. Along the way, we show that many of the classical functional equations satisfied by low-order polylogarithms (such as Spence-Kummer's equation of the trilogarithm or the tetralogarithmic one of Kummer) are of cluster type.
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Cited by 1 Pith paper
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A story of webs: the webs by conics on del Pezzo quartic surfaces and Gelfand-MacPherson's web of the spinor tenfold
The Gelfand-MacPherson 10-web on the quotient of the spinor tenfold carries a unique master 2-abelian relation that generates all weight-3 hyperlogarithmic functional identities of quartic del Pezzo surfaces.
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