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Mar 27, 2023 at 23:06 comment added LSpice I am confused about the statement that we can order the simple roots so that the bilinear form is invariant under diagram automorphisms. Suppose that we are in type $\mathsf A_2$. Then, however we number them, there is a diagram automorphism switching $\alpha_1$ and $\alpha_2$, but $B(\alpha_1, \alpha_2) = 0$, while $B(\alpha_2, \alpha_1) = -1$.
Mar 30, 2016 at 14:13 history answered Marty CC BY-SA 3.0