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Article Dans Une Revue Advances in Mathematics Année : 2019

On parabolic subgroups of Artin-Tits groups of spherical type

Résumé

We show that, in an Artin-Tits group of spherical type, the intersection of two parabolic subgroups is a parabolic subgroup. Moreover, we show that the set of parabolic subgroups forms a lattice with respect to inclusion. This extends to all Artin-Tits groups of spherical type a result that was previously known for braid groups. To obtain the above results, we show that every element in an Artin-Tits group of spherical type admits a unique minimal parabolic subgroup containing it. Also, the subgroup associated to an element coincides with the subgroup associated to any of its powers or roots. As a consequence, if an element belongs to a parabolic subgroup, all its roots belong to the same parabolic subgroup.

Dates et versions

hal-01684387 , version 1 (15-01-2018)

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Citer

María Cumplido Cabello, Volker Gebhardt, Juan González-Meneses, Bert Wiest. On parabolic subgroups of Artin-Tits groups of spherical type. Advances in Mathematics, 2019, 352, pp.572-610. ⟨10.1016/j.aim.2019.06.010⟩. ⟨hal-01684387⟩
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