Representations of the symmetric group which are irreducible over subgroups

J. Brundan and A. S. Kleshchev

Abstract. Let $F$ be an algebraically closed field of characteristic $p$, and
$\Sigma_n$ be the symmetric group on $n$ letters. In this paper we classify
all pairs $(G,D)$, where $D$ is an irreducibe $F\Sigma_n$-module of dimension
greater than $1$ and $G$ is a proper subgroup of $\Sigma_n$ such that the
restriction $D\!\downarrow_G$ is irreducible, provided $p > 3$.