Title: Evaluating Characteristic Functions of Character Sheaves at Unipotent
Elements

Author: Jay Taylor

Abstract: Assume $\bG$ is a connected reductive algebraic group defined over an
algebraic closure $\mathbb{K} = \overline{\mathbb{F}}_p$ of the finite field of
prime order $p>0$. Furthermore, assume that $F : \bG \to \bG$ is a Frobenius
endomorphism of $\bG$. In this article we give a formula for the value of any
$F$-stable character sheaf of $\bG$ at a unipotent element. This formula is
expressed in terms of class functions of $\bG^F$ which are supported on a
single unipotent class of $\bG$. In general these functions are not determined,
however we give an expression for these functions under the assumption that
$Z(\bG)$ is connected, $\bG/Z(\bG)$ is simple and $p$ is a good prime for
$\bG$. In this case our formula is completely explicit.