Constructing characters of Sylow p-subgroups of finite Chevalley groups

Simon M. Goodwin, Tung Le, Kay Magaard, Alessandro Paolini

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)
223 Downloads (Pure)

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 languageEnglish
Pages (from-to)395–439
Number of pages45
JournalJournal of Algebra
Volume468
Early online date31 Aug 2016
DOIs
Publication statusPublished - 15 Dec 2016

Keywords

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

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