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

Fuente: arXiv
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Main Author: Stewart, David I.
Format: Preprint
Published: 2015
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author Stewart, David I.
author_facet Stewart, David I.
contents 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>.
format Preprint
id arxiv_https___arxiv_org_abs_1508_02918
institution arXiv
publishDate 2015
record_format arxiv
spellingShingle On the minimal modules for exceptional Lie algebras: Jordan blocks and stabilisers
Stewart, David I.
Representation Theory
Group Theory
Rings and Algebras
17B45, 20G15
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>.
title On the minimal modules for exceptional Lie algebras: Jordan blocks and stabilisers
topic Representation Theory
Group Theory
Rings and Algebras
17B45, 20G15
url https://arxiv.org/abs/1508.02918