Standard Action

Every finite Coxeter group W has a standard action. For example, the standard action group of a Coxeter group of type A_n is the symmetric group of degree n + 1 acting on {1, ..., n}.

StandardAction(W) : GrpFPCox -> Map

StandardAction(W) : GrpPermCox -> Map

The standard action of the finite Coxeter group W.

StandardActionGroup(W) : GrpFPCox -> GrpPerm, Map

StandardActionGroup(W) : GrpPermCox -> GrpPerm, Map

The group G of the standard action of the finite Coxeter group W, together with an isomorphism W to G.

> W := CoxeterGroup("A3");
> G, h := StandardActionGroup(W);
> IsSymmetric(G);
true
> h(W.1); h(W.2); h(W.3);          
(1, 2)
(2, 3)
(3, 4)