B2 weight lattice
= B2 weight lattice
{c}
{title2=$P(B_2)=\mathbb Z^2\cup(\mathbb Z+\frac12)^2$}
For simple roots $(1,0)$ and $(-1,1)$, <coroot> integrality gives the <weight lattice> $P=\mathbb Z^2\cup(\mathbb Z+1/2)^2$. This is the lattice for the <Spin group> $\operatorname{Spin}(5)$ and its <Lie algebra>. Representations descending to $SO(5)$ use the integer coset, because a $2\pi$ rotation in either coordinate plane must act trivially.