On the minimal modules for exceptional Lie algebras: Jordan blocks and stabilisers
Representation Theory
2024-04-24 v6 Group Theory
Rings and Algebras
Abstract
Let G be a simple simple-connected exceptional algebraic group of type G_2, F_4, E_6 or E_7 over an algebraically closed field k of characteristic p>0 with \g=Lie(G). For each nilpotent orbit G.e of \g, we list the Jordan blocks of the action of e on the minimal induced module V_min of \g. We also establish when the centralisers G_v of vectors v\in V_min and stabilisers \Stab_G<v> of 1-spaces <v>\subset V_min are smooth; that is, when \dim G_v=\dim\g_v or \dim \Stab_G<v>=\dim\Stab_\g<v>.
Keywords
Cite
@article{arxiv.1508.02918,
title = {On the minimal modules for exceptional Lie algebras: Jordan blocks and stabilisers},
author = {David I. Stewart},
journal= {arXiv preprint arXiv:1508.02918},
year = {2024}
}
Comments
This contains corrections and should be used instead of the published version ; code now available at github.com/davistem/nilpotent_orbits_GAP