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arXiv · 2312.00697

Motivic coaction and single-valued map of polylogarithms from zeta generators

Hadleigh Frost·Martijn Hidding·Deepak Kamlesh·Carlos Rodriguez·Oliver Schlotterer·Bram Verbeek
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Abstract

We introduce a new Lie-algebraic approach to explicitly construct the motivic coaction and single-valued map of multiple polylogarithms in any number of variables. In both cases, the appearance of multiple zeta values is controlled by conjugating generating series of polylogarithms with Lie-algebra generators associated with odd zeta values. Our reformulation of earlier constructions of coactions and single-valued polylogarithms preserves choices of fibration bases, exposes the correlation between multiple zeta values of different depths and paves the way for generalizations beyond genus zero.

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Hadleigh Frost, Martijn Hidding, Deepak Kamlesh, Carlos Rodriguez, Oliver Schlotterer, Bram Verbeek. 2023-12-01. Motivic coaction and single-valued map of polylogarithms from zeta generators. https://arxiv.org/abs/2312.00697

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