atlas Library · Script File
nilpotent_orbits_exceptional.at
lists of 1/2 h(O^\vee) for exceptional groups
exceptional groups first
nilpotent orbit given by labelled Dynkin diagram
label c={0,1,2} on node i -> (c/2)*i^th fundamental weightDefinitions in source order
nilpotent_lambdas_G2
L9
nilpotent_lambdas_G2 = [ratvec]these are flipped from the table Carter due to the dualityL12
nilpotent_lambdas_F4
L14
nilpotent_lambdas_F4 = [ratvec]nilpotent_lambdas_E6
L33
nilpotent_lambdas_E6 = [ratvec]nilpotent_lambdas_E7
L57
nilpotent_lambdas_E7 = [ratvec]nilpotent_lambdas_E8
L105
nilpotent_lambdas_E8 = [ratvec]nilpotent_lambdas_E
L178
nilpotent_lambdas_E (int n) = [ratvec]nilpotent_lambdas
L184
nilpotent_lambdas (RootDatum rd) = [ratvec]this assumes |rd| is simple
Generated from atlas-scripts at commit 648506c (2026-10-13).