On parabolic closures in Coxeter groups

Abstract

For a finitely generated subgroup W′ of a Coxeter system (W, S), there are finitely generated reflection subgroups W1, . . . , Wn of W, each containing W′, such that any reflection subgroup of W containing W′ contains one of the Wi as a standard parabolic subgroup. The canonical Coxeter generators of the Wi , and an expression for the parabolic closure of W′ as a W-conjugate of a standard parabolic subgroup of W, may be effectively determined.