Characters of the Grothendieck-Teichmueller group through rigidity of the Burau representation

Details Characters of the Grothendieck-Teichmueller group through rigidity of the Burau representation Characters of the Grothendieck-Teichmueller group through rigidity of the Burau representation

2008-01-16

arxiv.org/abs/0801.2507v1

Mathematics

Representation Theory

Scientific paper

We present examples of characters of absolute Galois groups of number fields that can be recovered through their action by automorphisms on the profinite completion of the braid groups, using a ``rigidity'' approach. The way we use to recover them is through classical representations of the braid groups, and in particular through the Burau representation. This enables one to extend these characters to Grothendieck-Teichmueller groups.

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