Representations of Lie superalgebras in prime characteristic I

We initiate the representation theory of restricted Lie superalgebras over an algebraically closed field of characteristic p > 2. A superalgebra generalization of the celebrated Kac–Weisfeiler conjecture is formulated, which exhibits a mixture of p-power and 2-power divisibilities of dimensions of modules. We establish the conjecture for basic classical Lie superalgebras.