On the $p$-defect of character degrees of finite groups of Lie type

Abstract

This paper is concerned with the representation theory of finite groups. According to Robinson, the truth of certain variants of Alperin's weight conjecture on the $p$-blocks of a finite group would imply some arithmetical conditions on the degrees of the irreducible (complex) characters of that group. The purpose of this note is to prove directly that one of these arithmetical conditions is true in the case where we consider a finite group of Lie type in good characteristic.