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      Constructing characters of Sylow \(p\)-subgroups of finite Chevalley groups

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          Abstract

          Let \(q\) be a power of a prime \(p\), let \(G\) be a finite Chevalley group over \(\mathbb{F}_q\) 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 \(\mathrm{F}_4\), 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.

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          Journal
          2015-12-08
          Article
          1512.02678
          36594679-157d-4c45-898a-4e81ca07f2a7

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          37 pages
          math.RT math.GR

          Algebra
          Algebra

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