### 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 2010 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*American Journal of Mathematics*,

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

**Representations of the general linear groups which are irreducible over subgroups.** / Kleshchev, Alexander S.; Tiep, Pham Huu.

Research output: Contribution to journal › Article

*American Journal of Mathematics*, vol. 132, no. 2, pp. 425-473. https://doi.org/10.1353/ajm.0.0108

}

TY - JOUR

T1 - Representations of the general linear groups which are irreducible over subgroups

AU - Kleshchev, Alexander S.

AU - Tiep, Pham Huu

PY - 2010/4

Y1 - 2010/4

N2 - We classify all triples (G, V,H) such that SLn(q) ≤ G ≤ GLn(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.

AB - We classify all triples (G, V,H) such that SLn(q) ≤ G ≤ GLn(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.

UR - http://www.scopus.com/inward/record.url?scp=77951061685&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77951061685&partnerID=8YFLogxK

U2 - 10.1353/ajm.0.0108

DO - 10.1353/ajm.0.0108

M3 - Article

VL - 132

SP - 425

EP - 473

JO - American Journal of Mathematics

JF - American Journal of Mathematics

SN - 0002-9327

IS - 2

ER -