Galois actions on complex braid groups

TL;DR

This paper demonstrates a faithful geometric action of the absolute Galois group on discriminantal varieties linked to complex reflection groups, exploring potential connections with the profinite Grothendieck-Teichmüller group.

Contribution

It establishes the faithfulness of Galois actions on complex braid groups and reviews their connections with the Grothendieck-Teichmüller group.

Findings

Proves faithfulness of Galois action on discriminantal varieties

Connects Galois actions with complex reflection groups

Discusses potential links to Grothendieck-Teichmüller group

Abstract

We establish the faithfulness of a geometric action of the absolute Galois group of the rationals that can be defined on the discriminantal variety associated to a finite complex reflection group, and review some possible connections with the profinite Grothendieck-Teichm\"uller group.