ScalingStacks

Remark 6.2.6. The bilinear form $\langle\langle-,-\rangle\rangle:R_{n}\times R_{n}\to\frac{1}{2}{\mathbf{Z}}$ obtained from $\langle-,-\rangle$ by composing with the morphism $L_{n}\to\frac{1}{2}{\mathbf{Z}},\ \varepsilon_{i}\mapsto-\frac{1}{2}$ is given by $\langle\langle\alpha_{a},\alpha_{b}\rangle\rangle=\frac{1}{2}(\delta_{b,a+1}-\delta_{b+1,a})$. It is antisymmetric.