Talk:Weight (representation theory)

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Please, could somebody check the information in this page? I'm not sure about the definition of G-integral weight for a Lie group G. How much important is that G is semisimple? Does the definition make reasonable sense for non-semisimple groups as well? Further, in the definition of a weight of a Lie group, is it reasonable to assume that H is a maximal commutative subgroup? Would it not be better to assume a maximal commutative torus (I think for G complex semisimple, it is the same)? Please, fix these subtle issues, if you are an expert! Thank u, Peter

Well, if G is compact one should take H to be a maximal torus (every maximal torus is a maximal abelian subgroup but not vice-versa). I'm not sure what the correct choice is for G noncompact. Maybe a maximal closed, connected abelian subgroup? I'll work on this page if time permits, but I'm not an expert either. -- Fropuff 22:40, 27 September 2006 (UTC)

I see no explanation here of how the roots are chosen for a given Lie algebra. The ideas of weights and roots need to be connected.Dewa 20:27, 24 February 2007 (UTC)


[edit] Merge weight space into weight (representation theory)

These are from the Talk:weight space page:

Weight space is a common term in representation theory, but maybe it should be merged with the article weight (representation theory), where all the information are contained. Franp9am 18:34, 8 November 2007 (UTC)

Thanks for cleaning up most of the simple issues with this article. I tried continuing your work, and I have to agree with the merger. The problems with this article are almost all already handled in the regular weight article. In fact, treating weights as generalized eigenvalues, this is just a separate article on eigenspaces. However, notice that eigenvector, eigenvalue, and eigenspace all redirect to the same article. Perhaps the same should be done here for weight space, weight vector, and weight (representation theory). I think weight (representation theory) is a nice name for the combined article, and it is already there.
If you would like, I can add the {{mergeto}} and {{mergefrom}} tags to more formally suggest the merger. I doubt anyone will have any objection, but its good to give some time for comments. JackSchmidt 20:06, 12 November 2007 (UTC)

I never heard back from Franp9am, so went ahead and added the tags. JackSchmidt (talk) 18:09, 19 November 2007 (UTC)

I added a few more very short articles on specific aspects of weights to the merge list. Most are already contained in this article. One might want to consider fundamental representation as well, though it is reasonably full and its short companion article fundamental weight is already merged into this article. JackSchmidt (talk) 01:11, 22 November 2007 (UTC)