A standard parabolic subgroup of a Coxeter group is a subgroup generated by a subset of its Coxeter generating set. The maximal parabolic subgroups are those that come from omitting a single Coxeter generator. In S ~ ~ n , all maximal parabolic subgroups are isomorphic to the finite symmetric group S n . The subgroup generated by the subset { s 0 , … … , s n − − 1 } ∖ ∖ { s i } consists of those affine permutations that stabilize the interval [ i + 1 , i + n ] , that is, that map every element of this interval to another element of the interval.