On Quasi Steinberg characters of Complex Reflection Groups

Ashish Mishra; Digjoy Paul; Pooja Singla

On Quasi Steinberg characters of Complex Reflection Groups

Representation Theory 2022-07-05 v1

Authors: Ashish Mishra , Digjoy Paul , Pooja Singla

Abstract

Let $G$ be a finite group and $p$ be a prime number dividing the order of $G$ . An irreducible character $\chi$ of $G$ is called a quasi $p$ -Steinberg character if $\chi(g)$ is nonzero for every $p$ -regular element $g$ in $G$ . In this paper, we classify quasi $p$ -Steinberg characters of the complex reflection groups $G(r,q,n)$ . In particular, we obtain this classification for Weyl groups of type $B_n$ and type $D_n$ .

Keywords

character theory character theory of finite groups finite groups

Cite

@article{arxiv.2207.01564,
  title  = {On Quasi Steinberg characters of Complex Reflection Groups},
  author = {Ashish Mishra and Digjoy Paul and Pooja Singla},
  journal= {arXiv preprint arXiv:2207.01564},
  year   = {2022}
}

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14 pages. Comments welcome

On Quasi Steinberg characters of Complex Reflection Groups

Abstract

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