> I just tried to get the degrees of the fundamental invariants of a
> CoxeterGroup or WeylGroup. Does anyone know how to get them?
For Weyl groups are tabulated in the Appendices to Bourbaki, Groupes
et Algebres de Lie Ch 4-6.
For other Coxeter groups, they are in Coxeter, The product of the
generators of a finite group generated
by reflections. Duke Math. J. 18, (1951). 765--782.
At least for the classical Cartan types it might be natural to add
them as methods
in the ambient space. So you could:
sage: L=RootSystem("E8").ambient_space()
sage: L.invariant_degrees()
[1,7,11,13,17,19,23,29]
Here is a related thread:
http://mathoverflow.net/questions/37602/polynomial-invariants-of-the-exceptional-weyl-groups
Dan
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