- #1
spookyfish
- 53
- 0
If [itex]\alpha [/itex] and [itex]\beta [/itex] are simple roots, then [itex]\alpha-\beta [/itex] is not. This means that
[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.
[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.