Counting characters in linear group actions

Details Counting characters in linear group actions Counting characters in linear group actions

2007-04-04

arxiv.org/abs/0704.0581v1

Mathematics

Representation Theory

Scientific paper

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 $\chi\in\Irr(GV)$ such that, for a fixed $v\in V$, the restriction of
$\chi$ to $$ is not a multiple of the regular character of $$. These
results might be useful in attacking the non--coprime $k(GV)$--problem.

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