Irreducible representations of finite exceptional groups of lie type containing matrices with simple spectra

Abstract

Absolutely irreducible representations of finite groups of exceptional Lie types in defining characteristic whose images contain matrices with simple spectra are determined. The term ”simple spectrum“ means that each eigenvalue has multiplicity 1. The similar question for the classical finite groups has been solved in the authors' previous paper [Comm. in Algebra 26 (1998), no 3, 863-888] where one can find general comments to the problem. For dimensions ≥ 100 all absolutely irreducible representations of finite groups of Lie type in defining characteristic containing matrices with simple spectra are tabulated.