Irreducible A_1 Subgroups of Exceptional Algebraic Groups
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2015
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| _version_ | 1866916407316316160 |
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| author | Thomas, Adam |
| author_facet | Thomas, Adam |
| contents | A closed subgroup of a semisimple algebraic group is called irreducible if it lies in no proper parabolic subgroup. In this paper we classify all irreducible $A_1$ subgroups of exceptional algebraic groups $G$. Consequences are given concerning the representations of such subgroups on various $G$-modules: for example, the conjugacy classes of irreducible $A_1$ subgroups are determined by their composition factors on the adjoint module of $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1501_04858 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | Irreducible A_1 Subgroups of Exceptional Algebraic Groups Thomas, Adam Group Theory 20G41, 20G15, 20G05 A closed subgroup of a semisimple algebraic group is called irreducible if it lies in no proper parabolic subgroup. In this paper we classify all irreducible $A_1$ subgroups of exceptional algebraic groups $G$. Consequences are given concerning the representations of such subgroups on various $G$-modules: for example, the conjugacy classes of irreducible $A_1$ subgroups are determined by their composition factors on the adjoint module of $G$. |
| title | Irreducible A_1 Subgroups of Exceptional Algebraic Groups |
| topic | Group Theory 20G41, 20G15, 20G05 |
| url | https://arxiv.org/abs/1501.04858 |