G2 root system
= G2 root system
{c}
{title2=$G_2$}
{wiki=G2_(mathematics)}
The $G_2$ root system has six short and six long roots. For a short simple root $\alpha_1$ and a long simple root $\alpha_2$, its positive roots are
$$
\alpha_1,\ \alpha_2,\ \alpha_1+\alpha_2,\ 2\alpha_1+\alpha_2,\ 3\alpha_1+\alpha_2,\ 3\alpha_1+2\alpha_2.
$$