Green Functions in Small Characteristic

Abstract

The values of the ordinary Green functions are known for almost all groups of Lie type, a long term achievement by various authors. In this note we solve the last open cases, which are for exceptional groups $E_8(q)$ where $q$ is a power of $2$, $3$ or $5$.

Corrected a few misprints in the previous revision (most importantly some wrong indices in the last two subsections)