Parabolic subgroups of large-type Artin groups

María Cumplido Cabello, Alexandre Martin, Nicolas Vaskou

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
48 Downloads (Pure)

Abstract

We show that the geometric realisation of the poset of proper parabolic subgroups of a large-type Artin group has a systolic geometry. We use this geometry to show that the set of parabolic subgroups of a large-type Artin group is stable under arbitrary intersections and forms a lattice for the inclusion. As an application, we show that parabolic subgroups of large-type Artin groups are stable under taking roots and we completely characterise the parabolic subgroups that are conjugacy stable.

We also use this geometric perspective to recover and unify results describing the normalisers of parabolic subgroups of large-type Artin groups.
Original languageEnglish
Pages (from-to)393-414
Number of pages22
JournalMathematical Proceedings of the Cambridge Philosophical Society
Volume174
Issue number2
Early online date12 Sept 2022
DOIs
Publication statusPublished - Mar 2023

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