Parabolic subgroup of a reflection group

In the mathematical theory of reflection groups, the parabolic subgroups are a special kind of subgroup. The precise definition of which subgroups are parabolic depends on context—for example, whether one is discussing general Coxeter groups or complex reflection groups—but in all cases the collection of parabolic subgroups exhibits important good behaviors. For example, the parabolic subgroups of a reflection group have a natural indexing set and form a lattice when ordered by inclusion. The different definitions of parabolic subgroups essentially coincide in the case of finite real reflection groups. Parabolic subgroups arise in the theory of algebraic groups, through their connection with Weyl groups.

This keyword could refer to multiple things. Here are some suggestions: