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

Matthieu Calvez (1) , Bruno Aaron Cisneros de La Cruz (2) , María Cumplido Cabello (3, 4)

1 Departamento de Matemáticas [Valparaíso]
2 Instituto de Matemáticas de la UNAM [Oaxaca]
3 IMB - Institut de Mathématiques de Bourgogne [Dijon]
4 Department of Actuarial Mathematics and Statistics, Heriot-Watt University

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 Gonzalez-Meneses in the specific case of Artin braid groups.

Mots clés: Artin-Tits group; Conjugacy stability; Parabolic subgroups

Domaines: Mathématiques [math]

Matthieu Calvez, Bruno Aaron Cisneros de La Cruz, María Cumplido Cabello. Conjugacy stability of parabolic subgroups of Artin-Tits groups of spherical type. Journal of Algebra, 2020, 556, pp.621-633. ⟨10.1016/j.jalgebra.2020.03.017⟩. ⟨hal-03023797⟩