  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.
