The vectors [itex]\vec{\alpha}=\{\alpha_1,\ldots\alpha_m \}[/itex] are defined by(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

[H_i,E_\alpha]=\alpha_i E_\alpha

[/tex]

they are also known to be the non-zero weights, called the roots, in the adjoint representation. My question is - is this connection (that the vectors [itex]\vec{\alpha} [/itex] defined by the commutation relations above in some representation, are also the roots of the adjoint representation) is true only when [itex]\vec{\alpha} [/itex] is in the defining representation, or is it true for any representation?

I hope my question is clear

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# Lie group representations

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