Semidirect product decomposition of Coxeter groups

Cédric Bonnafé, Matthew J. Dyer

Let $(W,S)$ be a Coxeter system, let $S=I\dot{\cup }J$ be a partition of $S$ such that no element of $I$ is conjugate to an element of $J$, let $\tilde{J}$ be the set of $W_I$…