Unisingular representations of finite symplectic groups

Abstract

Let G be a group and ρ an irreducible representation of G. Then ρ is called unisingular if $\rho (g)$ has eigenvalue 1 for every $g\in G.$ In this paper we determine the unisingular 2-modular irreducible representations of the symplectic group over the field of two elements. A similar problem is solved for the maximal tori of G.

Keywords:

• 2-modular representations
• eigenvalue 1
• maximal tori
• semisimple elements
• symplectic group

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 20G05
• 20G40