Representations of Lie superalgebras in prime characteristic II: The queer series

The modular representation theory of the queer Lie superalgebra q(n) over characteristic p>2 is developed. We obtain a criterion for the irreducibility of baby Verma modules with semisimple p-characters and a criterion for the semisimplicity of the corresponding reduced enveloping algebras. A (2p)-power divisibility of dimensions of q(n)-modules with nilpotent p-characters is established. The representation theory of q(2) is treated in detail. We formulate a Morita super-equivalence conjecture for q(n) with general p-characters which is verified for n=2.