Counting characters in linear group actions
Thomas Michael Keller · arXiv (Cornell University) · 2007
Let $G$ be a finite group and $V$ be a finite $G$--module. We present upper bounds for the cardinalities of certain subsets of $\Irr(GV)$, such as the set of those $χ\in\Irr(GV)$ such that, for a fixed $v\in V$, the restriction of $χ$ to $$ is not a multiple of the regular character of $$. These results might be useful in attacking the non--coprime $k(GV)$--problem.