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For the B2 root system with ${\alpha }_1$ short, the positive roots areSubstituting $\lambda =a{\omega }_1+b{\omega }_2$ into the Weyl dimension formula for B2 gives

Realize the B2 root system in ${\mathbb{R}}^2$ asChoose the short simple root and long simple rootThenas follows from $⟨{\omega }_i,{\alpha }_j^{\vee }⟩={\delta }_{ij}$. The roots form a square from the long roots with the four short roots on the coordinate axes; the double edge in the Dynkin diagram points toward ${\alpha }_1$.

The positive roots areFor $\lambda =a{\omega }_1+b{\omega }_2$, substituting their coroot pairings in the Weyl dimension formula givesThis is the Weyl dimension formula for B2.