On the minimal modules for exceptional Lie algebras: Jordan blocks and stabilisers
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arXiv
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| Format: | Preprint |
| Published: |
2015
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| _version_ | 1866929324468207616 |
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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 |