Unisingular irreducible representations of finite groups of Lie type in the natural characteristic

GRA2 - Groups, representations and applications: new perspectives

A linear representation $\rho$ of a group $G$ is called {\it unisingular} if every element of $G$ has eigenvalue 1. We are interested with the classification problem of unisingular representations $\rho$ for finite simple groups. In this talk we focus on the case where $G$ is a group of Lie type and $\rho$ is an irreducible representation over an algebraically closed field whose characteristic coincides with the defining characterisitic of $G$. There are a number of precise results and sufficient conditions to be discussed, and of open problems.

This talk is part of the Isaac Newton Institute Seminar Series series.