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Representations of the general linear groups which are irreducible over subgroups
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 132, Number 2, April 2010
- pp. 425-473
- 10.1353/ajm.0.0108
- Article
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We classify all triples $(G,V,H)$ such that $SL_n(q)\leq G\leq GL_n(q)$,
$V$ is a representation of $G$ of dimension greater than one over an
algebraically closed field ${\Bbb F}$ of characteristic prime to $q$, and $H$
is a proper subgroup of $G$ such that the restriction $V\downarrow_{H}$ is
irreducible. This problem is a natural part of the Aschbacher-Scott
program on maximal subgroups in finite classical groups.