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Standard Action

Every finite Coxeter group W has a standard action. For example, the standard action group of a Coxeter group of type An 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.

Example GrpCox_StandardAction (H98E30)

> 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)

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Version: V2.19 of Mon Dec 17 14:40:36 EST 2012