I'm currently searching, for quite a while now, for a paper/book that discusses symmetry breaking in terms of roots and weights.
Any suggestions would be much appreciated!
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$\begingroup$ I know of no resource, so just a nitpick on terminology: Roots are not generators, they live in the dual of the Cartan subalgebra, not in the whole Lie algebra (or its dual). $\endgroup$– ACuriousMind ♦Commented Jul 7, 2015 at 14:51
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$\begingroup$ @ACuriousMind Firstly, simply laced algebras are self dual and in physics we deal almost exclusively with simply laced algebras. Secondly, roots are generators. We label the elements of each representation by the Cartan generator eigenvalues. This gives us, in general, the weights that define the representation. For the adjoint rep the weights are called roots. The adjoint rep is the rep on the groups own Lie algebra and therefore roots are generators $\endgroup$– jakCommented Jul 7, 2015 at 14:53
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