Counting characters in linear group actions

Thomas Michael Keller

Counting characters in linear group actions

Representation Theory 2007-05-23 v1 Group Theory

Authors: Thomas Michael Keller

Abstract

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 $<v>$ is not a multiple of the regular character of $<v>$ . These results might be useful in attacking the non--coprime $k(GV)$ --problem.

Keywords

character theory character theory of finite groups combinatorial group theory

Cite

@article{arxiv.0704.0581,
  title  = {Counting characters in linear group actions},
  author = {Thomas Michael Keller},
  journal= {arXiv preprint arXiv:0704.0581},
  year   = {2007}
}

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