Long-root A2 subsystem of G2
= Long-root A2 subsystem of G2
{c}
{title2=$A_2\subset G_2$}
For short and long simple roots $\alpha,\beta$ of $G_2$, the long roots form an $A_2$ root system with simple roots $\delta_1=\beta$ and $\delta_2=3\alpha+\beta$. If $\omega_1,\omega_2$ are the corresponding $A_2$ <fundamental weights>, then $\alpha=\omega_2-\omega_1$ and $\alpha^\vee=\delta_2^\vee-\delta_1^\vee$.