Some matrix representations of the parameters of the Grothendieck-Teichmueller group

 

(Un exposé de H. Nakamura au séminaire de théorie des nombres de Chevaleret le 10 mars 2003)

Résumé :

It is well known that the absolute Galois group of
the rational number field is embedded in the
Grothendieck-Teichmueller group GT.
The main parameter of GT is valued in the free profinite
group of two variables. We specialize these variables
to certain 2 by 2 matrices, and find the parameter
images closely related with Anderson-Ihara's adelic
beta functions.