6533b820fe1ef96bd1279128

RESEARCH PRODUCT

Centralizers of Parabolic Subgroups of Artin Groups of TypeAl,Bl, andDl

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Abstract Let ( A , Σ) be an Artin system of one of the types A l , B l , D l . For X  ⊆ Σ, we denote by A X the subgroup of A generated by X . Such a group is called a parabolic subgroup of ( A , Σ). Let A X be a parabolic subgroup with connected associated Coxeter graph. We exhibit a generating set of the centralizer of A X in A . Moreover, we prove that there exists X ′ ⊆ Σ such that A X ′ is conjugate to A X and such that the centralizer of A X ′ in A is generated by the centers of all the parabolic subgroups containing A X ′ .