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June 2018 Fundamental Solutions of the Knizhnik-Zamolodchikov Equation of One Variable and the Riemann-Hilbert Problem
Shu OI, Kimio UENO
Tokyo J. Math. 41(1): 1-20 (June 2018). DOI: 10.3836/tjm/1502179274

Abstract

In this article, we show that the generalized inversion formulas of the multiple polylogarithms of one variable, which are generalizations of the inversion formula of the dilogarithm, characterize uniquely the multiple polylogarithms under certain conditions. This means that the multiple polylogarithms are constructed from the multiple zeta values. We call such a problem of determining certain functions a recursive Riemann-Hilbert problem of additive type. Furthermore we show that the fundamental solutions of the KZ equation of one variable are uniquely characterized by the connection relation between the fundamental solutions of the KZ equation normalized at $z=0$ and $z=1$ under some assumptions. Namely the fundamental solutions of the KZ equation are constructed from the Drinfel'd associator. We call this problem a Riemann-Hilbert problem of multiplicative type.

Citation

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Shu OI. Kimio UENO. "Fundamental Solutions of the Knizhnik-Zamolodchikov Equation of One Variable and the Riemann-Hilbert Problem." Tokyo J. Math. 41 (1) 1 - 20, June 2018. https://doi.org/10.3836/tjm/1502179274

Information

Published: June 2018
First available in Project Euclid: 26 January 2018

zbMATH: 06966856
MathSciNet: MR3830806
Digital Object Identifier: 10.3836/tjm/1502179274

Subjects:
Primary: 11G55, 34M50
Secondary: 11M06, 30E25, 32G34

Rights: Copyright © 2018 Publication Committee for the Tokyo Journal of Mathematics

JOURNAL ARTICLE
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Vol.41 • No. 1 • June 2018
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