> 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.
the math was not the problem, but thx anyway!
> 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]
I think they are not attached to a root system or to its ambient
space. In fact, by the classification theorem by Shephard and Todd,
they (and the codegrees as well) are defined for complex reflection
groups and they have very nice properties for Weyl groups, a little
less for finite Coxeter groups, even less for well-generated complex
reflection groups, and still some meaning for any complex reflection
groups (see e.g. the wiki page on complex reflection groups).
Do you think, they should be in the ambient space anyway?
Christian
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