Abstract
Let q be a power of a prime p, let G be a finite Chevalley group over Fq 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 F4, 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