Geometric interpretation of double shuffle relation for multiple L-values
Algebraic Geometry
2012-10-02 v3 Quantum Algebra
Abstract
This paper gives a geometric interpretation of the generalized (including the regularization relation) double shuffle relation for multiple -values. Precisely it is proved that Enriquez' mixed pentagon equation implies the relations. As a corollary, an embedding from his cyclotomic analogue of the Grothendieck-Teichmuller group into Racinet's cyclotomic double shuffle group is obtained. It cyclotomically extends the result of our previous paper and the project of Deligne and Terasoma which are the special case N=1 of our result.
Cite
@article{arxiv.1012.4911,
title = {Geometric interpretation of double shuffle relation for multiple L-values},
author = {Hidekazu Furusho},
journal= {arXiv preprint arXiv:1012.4911},
year = {2012}
}
Comments
19 pages, to appear in "Galois-Teichmuller theory and Arithmetic Geometry" (H.Nakamura, F.Pop, L.Schneps, A.Tamagawa eds.) Advanced Studies in Pure Mathematcs Vol.63