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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 weight
Source
atlas-scripts/nilpotent_orbits_exceptional.at (190 lines)
Definitions
7
Loads
Loaded by
representations.at

Definitions in source order

nilpotent_lambdas_G2

L9nilpotent_lambdas_G2 = [ratvec]
these are flipped from the table Carter due to the duality
L12

nilpotent_lambdas_F4

L14nilpotent_lambdas_F4 = [ratvec]

nilpotent_lambdas_E6

L33nilpotent_lambdas_E6 = [ratvec]

nilpotent_lambdas_E7

L57nilpotent_lambdas_E7 = [ratvec]

nilpotent_lambdas_E8

L105nilpotent_lambdas_E8 = [ratvec]

nilpotent_lambdas_E

L178nilpotent_lambdas_E (int n) = [ratvec]

nilpotent_lambdas

L184nilpotent_lambdas (RootDatum rd) = [ratvec]
this assumes |rd| is simple

Generated from atlas-scripts at commit 648506c (2026-10-13).