Centralizers of Parabolic Subgroups of Artin Groups of TypeAl,Bl, andDl Original Research Article

Let (A, Σ) be an Artin system of one of the typesAl,Bl,Dl. ForX subset of or equal to Σ, we denote byAXthe subgroup ofAgenerated byX. Such a group is called a parabolic subgroup of (A, Σ). LetAXbe a parabolic subgroup with connected associated Coxeter graph. We exhibit a generating set of the centralizer ofAXinA. Moreover, we prove that there existsX′ subset of or equal to Σ such thatAX′is conjugate toAXand such that the centralizer ofAX′inAis generated by the centers of all the parabolic subgroups containingAX′.