Irreducible restrictions of spin representations of symmetric and alternating groups

Let $\mathbb{F}$ be an algebraically closed field and $G$ be an almost quasi-simple group. An important problem in representation theory is to classify the subgroups $H<G$ and $\mathbb{F}G$-modules $L$ such that the restriction $L{\downarrow }_H$ is irreducible. This problem is a natural part of the program of describing maximal subgroups in finite classical groups. In this paper we investigate the case of the problem where $G$ is the Schur’s double cover of alternating or symmetric group.