On restrictions of modular spin representations of symmetric and alternating groups

Let double struck F sign be an algebraically closed field of characteristic p and 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 of H and double struck F signH-modules V such that the restriction V↓ _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 is the Schur's double cover  _n or Ŝ _n.