The Fixed-Point-Space Dimension Function for a Finite Group Representation
I. Martin Isaacs · Proceedings of the American Mathematical Society · 1989
Given a complex representation of a finite group $G$, construct the integer valued function $\alpha$ on $G$ by setting $\alpha (g)$ to be the dimension of the fixed-point-space of $g$ in the module corresponding to the given representation. Usually, $\alpha$ is not a generalized character of $G$ and for trivial reasons $|G|\alpha$ is always a generalized character. The main result of this paper is that $e\alpha$ is always a generalized character, where $e$ is the exponent of $G$.