The center of pure complex braid groups

François Digne (1) , Ivan Marin (2) , Jean Michel (2)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée
2 IMJ - Institut de Mathématiques de Jussieu

Broué, Malle and Rouquier conjectured in that the center of the pure braid group of an irreducible finite complex reflection group is cyclic. We prove this conjecture, for the remaining exceptional types, using the analogous result for the full braid group due to Bessis, and we actually prove the stronger statement that any finite index subgroup of such braid group has cyclic center.

Mots clés: reflection groups; braid groups; Garside structure

Domaines: Théorie des groupes [math.GR]

François Digne, Ivan Marin, Jean Michel. The center of pure complex braid groups. Journal of Algebra, 2011, 347 (1), pp.206-213. ⟨10.1016/j.jalgebra.2011.06.034⟩. ⟨hal-00576774v2⟩