Irreducible restrictions of Brauer characters of the Chevalley group G_2(q) to its proper subgroups

TL;DR

This paper investigates when irreducible representations of Chevalley groups G_2(q) and related groups remain irreducible upon restriction to their maximal subgroups, providing a detailed classification in various cases.

Contribution

It determines the conditions under which irreducible representations of G_2(q) and related groups remain irreducible when restricted to proper subgroups, extending previous understanding.

Findings

Identifies specific cases where restrictions are irreducible

Provides classification for G_2(q), ^2B_2(q), and ^2G_2(q)

Enhances understanding of subgroup representation restrictions

Abstract

Let $G_2(q)$ be the Chevalley group of type $G_2$ defined over a finite field with q=p^n elements, where p is a prime number and $n$ is a positive integer. In this paper, we determine when the restriction of an absolutely irreducible representation of $G$ in characteristic other than p to a maximal subgroup of $G_2(q)$ is still irreducible. Similar results are obtained for $^2B_2(q)$ and $^2G_2(q)$.