KZ equation on the moduli space ${\mathcal M}_{0,5}$ and the harmonic product of multiple polylogarithms

Details KZ equation on the moduli space ${\mathcal M}_{0,5}$ and the harmonic product of multiple polylogarithms KZ equation on the moduli space ${\mathcal M}_{0,5}$ and the harmonic product of multiple polylogarithms

2009-10-05

arxiv.org/abs/0910.0718v3

Mathematics

Quantum Algebra

42 pages, 4 figures

Scientific paper

In this article, we derive a system of functional relations called the generalized harmonic product relations for hyperlogarithms on the moduli space ${\mathcal M}_{0,5}$ and show that the relations contain the harmonic product of multiple polylogarithms. The generalized harmonic product relations are equivalent to the relations which come from two decompositions of the fundamental solution normalized at the origin of the KZ equation on ${\mathcal M}_{0,5}$.

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