Double shuffle relation for associators.

link: http://arxiv.org/abs/0808.0319
Abstract

It is proved that Drinfel'd's pentagon equation implies the generalized
double shuffle relation. As a corollary, an embedding from the
Grothendieck-Teichm\"uller group $GRT_1$ into Racinet's double shuffle group
$DMR_0$ is obtained, which settles the project of Deligne-Terasoma. It is also
proved that the gamma factorization formula follows from the generalized double
shuffle relation.