### Abstract

Let G be a simple algebraic group over an algebraically closed field K of characteristic p > 0, let H be a proper closed subgroup of G and let V be a nontrivial irreducible KG-module, which is p-restricted, tensor indecomposable and rational. Assume that the restriction of V to H is irreducible. In this paper, we study the triples (G, H, V ) of this form when G is a classical group and H is positive-dimensional. Combined with earlier work of Dynkin, Seitz, Testerman and others, our main theorem reduces the problem of classifying the triples (G, H, V ) to the case where G is an orthogonal group, V is a spin module and H normalizes an orthogonal decomposition of the natural KG-module.

Original language | English |
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Pages (from-to) | 1259-1309 |

Number of pages | 51 |

Journal | Mathematische Annalen |

Volume | 367 |

Issue number | 3 |

Early online date | 11 Jun 2016 |

DOIs | |

Publication status | Published - Apr 2017 |

### Keywords

- Primary 20G05
- Secondary 20E28
- 20E32

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## Profiles

## Dr Tim C Burness

- School of Mathematics - Reader in Pure Mathematics
- Pure Mathematics
- Algebra

Person: Academic , Member

## Cite this

Burness, T. C., Marion, C., & Testerman, D. (2017). On irreducible subgroups of simple algebraic groups.

*Mathematische Annalen*,*367*(3), 1259-1309. https://doi.org/10.1007/s00208-016-1432-z