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Dear GAP-Forum,

Is the Weylgroup W(E,7) available in GAP?

Best Regards

Eberhard Freitag

In GAP (currently only Version 3) there is the CHEVIE package which

contains constructers for Weyl groups and programs to deal with them.

(I see that this can be difficult to find out, since the group is

constructed with `CoxeterGroup' - probably we should add a help

section whose header contains the keyword `Weyl'. For now ask

`??Coxeter'.)

You may try the following example commands (and have a look at the

corresponding help pages):

RequirePackage("chevie");

e7 := CoxeterGroup("E", 7); # a permutation group on the roots

x := Random(e7);

CoxeterWord(e7, x);

PrintDynkinDiagram(e7);

u := ReflectionSubgroup(e7, [1,2,3,5,6,7]);

PrintDynkinDiagram(u);

Display(InductionTable(u, e7));

Please, ask if there are more questions.

With best regards, Frank

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