If [itex]\alpha [/itex] and [itex]\beta [/itex] are simple roots, then [itex]\alpha-\beta [/itex] is not. This means that(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

E_{-\vec{\alpha}}|E_{\vec{\beta}}\rangle = 0

[/tex]

Now, according to the text I read, this means that [itex]q [/itex] in the formula

[tex]

\frac{2\vec{\alpha}\cdot \vec{\mu}}{\vec{\alpha}^2}=-(p-q)

[/tex]

is zero, where [itex]\vec{\mu} [/itex] is a weight, and [itex]p[/itex] and [itex]q [/itex] are integers. I couldn't understand why [itex]q=0 [/itex], if someone could explain to me.

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# Simple roots Lie algebra

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