C2 root system
= C2 root system
{c}
{title2=$C_2$}
In an orthonormal basis $(\varepsilon_1,\varepsilon_2)$, the roots are $\pm(\varepsilon_1-\varepsilon_2)$, $\pm(\varepsilon_1+\varepsilon_2)$, $\pm2\varepsilon_1$, and $\pm2\varepsilon_2$. Choose <simple roots> $\alpha_1=\varepsilon_1-\varepsilon_2$ and $\alpha_2=2\varepsilon_2$, with $\alpha_1$ a <short root>. The <fundamental weights> are $\omega_1=\varepsilon_1$ and $\omega_2=\varepsilon_1+\varepsilon_2$.