University of Sydney Algebra Seminar

Oded Yacobi

Friday 14 November, 12-1pm, in SMRI Seminar Room (Macleay Building A12 Room 301)

Normalisers of parabolic subgroups and hyperplane arrangements

Consider a Coxeter group \(W\) and its associated reflection representation. The group elements which act by reflections define an arrangement of hyperplanes which is important in the general theory. For instance, the associated Artin-Tits group, i.e. generalised braid group, can be recovered from the topology of the arrangement. We’ll review this classical story and then describe a new parabolic version of it in the case when \(W\) is finite, which recovers normalisers of parabolic subgroups of Artin-Tits groups from a hyperplane arrangement recently introduced in works of Iyama and Wemyss. This is based on joint work with Owen Garnier, Ed Heng and Tony Licata: arXiv:2509.21915