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

Hung Ngoc Nguyen

paper

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

arXiv:0910.4994

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 $^{2} B_{2} (q)$ and $^{2} G_{2} (q)$ .

30 pages