Dihedral symmetries of multiple polylogarithms

This paper finds relationships between multiple polylogarithms with a dihedral group action on the arguments. I generalize the combinatorics developed in Gangl, Goncharov and Levin’s $R$-deco polygon representation of multiple polylogarithms to find these relations. These relations between $R$-deco polygons, and between $R$-deco polygons and iterated integrals, can only be defined up to a primitive co-ideal.

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Published 11 September 2013