Representations of Coxeter groups over fusion rings and hyperplane complements

Abstract

We study faithful realisations of Coxeter groups over fusion rings and study Vinberg systems associated to them. We show that they induce embeddings of hyperplane complements, which provide geometrical realisations of certain types of strong admissible (LCM) homomorphisms between Artin--Tits groups.

arXiv commentv2: Referee comments incorporated. To appear in J. Lond. Math. Soc. v1: Comments are more than welcomed!