Character Ratios for Exceptional Groups of Lie Type

Abstract

AbstractWe prove character ratio bounds for finite exceptional groups $G(q)$ of Lie type. These take the form $\dfrac{|\chi (g)|}{\chi (1)} \le \dfrac{c}{q^k}$ for all nontrivial irreducible characters $\chi$ and nonidentity elements $g$, where $c$ is an absolute constant, and $k$ is a positive integer. Applications are given to bounding mixing times for random walks on these groups and also diameters of their McKay graphs.