## Abstract

Let

*q*be a power of a prime*p*, let*G*be a finite Chevalley group over F_{q}and let*U*be a Sylow*p*-subgroup of*G*; we assume that*p*is not a very bad prime for*G*. We explain a procedure of reduction of irreducible complex characters of*U*, which leads to an algorithm whose goal is to obtain a parametrization of the irreducible characters of*U*along with a means to construct these characters as induced characters. A focus in this paper is determining the parametrization when*G*is of type F_{4}, where we observe that the parametrization is "uniform" over good primes p > 3, but differs for the bad prime p = 3. We also explain how it has been applied for all groups of rank 4 or less.Original language | English |
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Pages (from-to) | 395–439 |

Number of pages | 45 |

Journal | Journal of Algebra |

Volume | 468 |

Early online date | 31 Aug 2016 |

DOIs | |

Publication status | Published - 15 Dec 2016 |

## Keywords

- math.RT
- math.GR
- Characters
- Chevalley groups
- Sylow p-subgroups

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