## Abstract

Let G be a finite group of Lie type in characteristic p. This paper addresses the problem of describing the irreducible complex (or p-adic) representations of G that remain absolutely irreducible under the Brauer reduction modulo p. An efficient approach to solve this problem for p > 3 has been elaborated in earlier papers by the authors. In this paper, we use arithmetical properties of character degrees to solve this problem for the groups G ∈ {^{2}B_{2}(q), ^{2}G_{2}(q), G_{2}(q), ^{2}F_{4}(q), F_{4}(q), ^{3}D_{4}(q)} provided that p ≤ 3. We also prove an asymptotical result, which solves the problem for all finite groups of Lie type over double-struck F sign_{q} with q large enough.

Original language | English (US) |
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Pages (from-to) | 3177-3184 |

Number of pages | 8 |

Journal | Proceedings of the American Mathematical Society |

Volume | 130 |

Issue number | 11 |

DOIs | |

State | Published - Nov 1 2002 |

## Keywords

- Finite groups of Lie type
- Reduction modulo p
- Steinberg representation

## ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics