### Abstract

We classify all triples (G, V,H) such that SL_{n}(q) ≤ G ≤ GL_{n}(q), V is a representation of G of dimension greater than one over an algebraically closed field F of characteristic prime to q, and H is a proper subgroup of G such that the restriction V↓_{H} is irreducible. This problem is a natural part of the Aschbacher-Scott program on maximal subgroups in finite classical groups.

Original language | English (US) |
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Pages (from-to) | 425-473 |

Number of pages | 49 |

Journal | American Journal of Mathematics |

Volume | 132 |

Issue number | 2 |

DOIs | |

State | Published - Apr 1 2010 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Kleshchev, A. S., & Tiep, P. H. (2010). Representations of the general linear groups which are irreducible over subgroups.

*American Journal of Mathematics*,*132*(2), 425-473. https://doi.org/10.1353/ajm.0.0108