A2 fundamental weights and weight lattice
= A2 fundamental weights and weight lattice
{c}
{title2=$\omega_1=(2\alpha_1+\alpha_2)/3,\quad\omega_2=(\alpha_1+2\alpha_2)/3$}
For the <A2 root system>, $\omega_1=(2\alpha_1+\alpha_2)/3$ and $\omega_2=(\alpha_1+2\alpha_2)/3$. The <weight lattice> $P=\mathbb Z\omega_1+\mathbb Z\omega_2$ contains the <root lattice> $Q$ with index three. In fundamental coordinates $(a,b)$, root-lattice membership is $a-b\equiv0\pmod3$.