On Quasi Steinberg characters of Complex Reflection Groups

TL;DR

This paper classifies quasi p-Steinberg characters of complex reflection groups, including Weyl groups of types B and D, revealing their structure and properties related to p-regular elements.

Contribution

It provides a complete classification of quasi p-Steinberg characters for complex reflection groups, extending understanding of their character theory and p-regular element interactions.

Findings

Classified quasi p-Steinberg characters for G(r,q,n)

Identified these characters for Weyl groups of types B and D

Enhanced understanding of character behavior on p-regular elements

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 $D_n$.