Parabolic subgroups of Artin groups of type FC

Let (A, S) be an Artin group of type FC and AT a standard parabolic subgroup of A. We use combinatorial tools to show that the normalizer of AT, the commensurator of AT, andthe product of the quasi-centralizer of AT by AT are equal. Furthermore, we show that the centralizer andthe quasi-centralizer of AT in A are generatedby their intersections with the monoid A +. 0. Introduction. Let S be a finite set and M =(ms,t)s,t∈S a symmetric matrix with ms,s =1 for s ∈ S and ms,t ∈ N −{0, 1} ∪ {∞} for s ̸ = t in S. An Artin-Tits system associated to M is the pair (AS,S) where AS is the group defined by the