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On the minimal modules for exceptional Lie algebras: Jordan blocks and stabilisers

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arxiv 1508.02918 v6 pith:6BSJ6AEJ submitted 2015-08-12 math.RT math.GRmath.RA

David I. Stewart This is my paper · ORCID
classification math.RTmath.GRmath.RA
keywords stabblocksexceptionaljordanminimalstabiliserswhenaction
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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>.

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  1. Small Lie algebras in the Verlinde category

    math.RT 2026-08 conditional novelty 7.0 of 10

    All simple based Lie algebras of length at most 3 in Ver_p are classified, along with all subalgebras from simple algebraic groups, resolving several conjectures.

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