Central-quotient dichotomy conjecture for irreducible Artin–Tits groups

Let $A_\Gamma$ be an irreducible Artin–Tits group, meaning that its defining graph $\Gamma$ does not decompose as a join of two non-empty subgraphs such that all edges between them are labeled by $2$, and let $Z(A_\Gamma)$ denote its center. The central quotient is $A_\Gamma/Z(A_\Gamma)$. Central-quotient dichotomy conjecture. The central quotient of every irreducible Artin–Tits group is either virtually cyclic or acylindrically hyperbolic. This conjecture concerns the classification of actions of irreducible Artin–Tits groups on hyperbolic spaces; the paper presents it as a main question, with the general case remaining open.