Communications in Number Theory and Physics
Volume 7 (2013)
Dihedral symmetries of multiple polylogarithms
Pages: 57 – 124
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.