Determination of Brauer Characters

Abstract

The purpose of this note is to show that the values of an irreducible (Brauer) character are the characteristic values of a matrix with non-negative rational integers. The construction of these integral matrices is done by a description of a representation of the Grothendieck ring of the category of modules over the group algebra. In particular a result of Solomon on characters and a result of Burnside on vanishing of a non-linear character on some conjugate class are generalized.