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arXiv · 2207.06528

On parabolic subgroups of Artin-Tits groups

Eddy Godelle
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Abstract

Abstract. We address the conjecture which states that an intersection of parabolic subgroups of an Artin-Tits group is a parabolic subgroup. We prove that the conjecture is equivalent to a, a priori, weaker conjecture. We also prove the conjecture in a specific case. Along the way, we provide short and almost self-contain algebraical proofs of several classical results on Artin-Tits groups, such as those of Van der Lek on intersection of standard parabolic subgroups.

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Eddy Godelle. 2022-07-13. On parabolic subgroups of Artin-Tits groups. https://arxiv.org/abs/2207.06528

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