Character of a representation

Summary

The character of a finite-dimensional group representation $\rho$ is the function $g \mapsto \tr \rho(g)$ on the group. It is constant on conjugacy classes, because the trace does not change under conjugation. For a finite group over the complex numbers, a representation is determined up to isomorphism by its character. So characters turn the study of representations into the study of a finite list of numbers.