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arXiv · 2011.04390

Unisingular representations in arithmetic and Lie theory

John Cullinan·Alexandre Zalesski
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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.

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John Cullinan, Alexandre Zalesski. 2020-11-09. Unisingular representations in arithmetic and Lie theory. https://arxiv.org/abs/2011.04390

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