Geometric interpretation of double shuffle relation for multiple L-values

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This paper gives a geometric interpretation of the generalized (including the regularization relation) double shuffle relation for multiple $L$-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.