Connection Problem of Knizhnik-Zamolodchikov Equation on Moduli Space ${\mathcal M}_{0,5}$

Shu Oi; Kimio Ueno

Connection Problem of Knizhnik-Zamolodchikov Equation on Moduli Space ${\mathcal M}_{0,5}$

Quantum Algebra 2011-10-18 v2 Algebraic Geometry Classical Analysis and ODEs Number Theory

Authors: Shu Oi , Kimio Ueno

Abstract

In this article, we consider the connection problem of the KZ (Knizhnik-Zamolodchikov) equation on the moduli space $\cM_{0,5}$ , and show that the connection matrices are expressed in terms of the Drinfel'd associator. As the compatibility condition on the connection problem, we have the pentagon relation for the Drinfeld associators. As an application of the connection problem, we derive the five term relation for dilogarithms.

Keywords

Knizhnik-Zamolodchikov equation connection problem moduli space Drinfel'd associator pentagon relation dilogarithm

Cite

@article{arxiv.1109.0715,
  title  = {Connection Problem of Knizhnik-Zamolodchikov Equation on Moduli Space ${\mathcal M}_{0,5}$},
  author = {Shu Oi and Kimio Ueno},
  journal= {arXiv preprint arXiv:1109.0715},
  year   = {2011}
}

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27 pages, 7 figures

Connection Problem of Knizhnik-Zamolodchikov Equation on Moduli Space ${\mathcal M}_{0,5}$

Abstract

Keywords

Cite

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