Coxeter groups in Coxeter groups

Abstract

An automorphism of a Coxeter diagram M leads in a natural way to a Coxeter subgroup of the Coxeter group of type M. We introduce admissible partitions of Coxeter diagrams in order to generalize this situation. An admissible partition of a Coxeter diagram provides a Coxeter subgroup in a similar way. Our main result is a local criterion for the admissibility of a partition.