Unisingular representations in arithmetic and Lie theory
Number Theory
2021-05-11 v2 Group Theory
Abstract
Let G be a subgroup of GL(V), where V is a finite dimensional vector space over a finite field of characteristic p >0. If det(g-1) = 0 for all g \in G then we call G a fixed-point subgroup of GL(V). Motivated in parallel by questions in arithmetic and linear group theory, we classify all irreducible fixed-point subgroups of Sp_8(2) and give new infinite series of irreducible fixed-point subgroups of symplectic groups Sp_m(2) for various m arising from certain representations of groups of Lie type.
Cite
@article{arxiv.2011.04390,
title = {Unisingular representations in arithmetic and Lie theory},
author = {John Cullinan and Alexandre Zalesski},
journal= {arXiv preprint arXiv:2011.04390},
year = {2021}
}
Comments
21 pages. Lemma 3.1 is is no longer "if and only if", which does not affect the main results. Other minor typos corrected