Conjugacy stability of parabolic subgroups of Artin-Tits groups of spherical type

TL;DR

This paper classifies conjugacy stable parabolic subgroups in Artin-Tits groups of spherical type, answering a key open question and extending previous results from braid groups to a broader class.

Contribution

It provides a complete classification of conjugacy stable parabolic subgroups in Artin-Tits groups of spherical type, generalizing prior work on braid groups.

Findings

Complete classification of conjugacy stable parabolic subgroups

Answers a question posed by Ivan Marin

Extends results from braid groups to all spherical type Artin-Tits groups

Abstract

We give a complete classification of conjugacy stable parabolic subgroups of Artin-Tits groups of spherical type. This answers a question posed by Ivan Marin and generalizes a theorem obtained by Juan Gonz\'alez-Meneses in the specific case of Artin braid groups.