On restrictions of modular spin representations of symmetric and alternating groups

Source abstract

Let F \mathbb F be an algebraically closed field of characteristic p p and H H be an almost simple group or a central extension of an almost simple group. An important problem in representation theory is to classify the subgroups G G of H H and F H \mathbb F H -modules V V such that the restriction V ↓ G V{\downarrow }_G is irreducible. For example, 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 H H is the Schur’s double cover A ^ n \hat A_n or S ^ n \hat S_n .