Irreducible restrictions of spin representations of symmetric and alternating groups

Abstract Let F ${\mathbb F}$ double struck upper F be an algebraically closed field and G $G$ upper G be an almost quasi-simple group. An important problem in representation theory is to classify the subgroups H G $H upper H less than upper G and F G ${\mathbb F} G$ double struck upper F upper G -modules L $L$ upper L such that the restriction L ↓ H $L{{\downarrow }}_H$ upper L down arrow Subscript upper H Baseline 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 $G$ upper G is the Schur’s double cover of an alternating or symmetric group.