Restricted representations of the Witt superalgebras

Let k be an algebraically closed field of characteristic p>3, and W(n) the superversion of the Witt algebra over k, i.e. the Lie superalgebra of superderivations of the Grassmann algebra of rank n over k. The simple modules and projective indecomposable modules in the restricted supermodule category for W(n) are studied. The character formulas for such simple modules are given, and the Cartan invariants for this category are presented.