For a type I basic classical Lie superalgebra g = g0̄⊕g1̄, we establish an equivalence between typical blocks of categories of Uχ(g)-modules and Uχ(g0̄)modules. We then deduce various consequences from the equivalence.

The composition factors of Kac-modules for the general linear Lie superalgebra gl m|n is explicitly determined. In particular, a conjecture of Hughes, King and van der Jeugt in [J. Math. Phys., 41 (2000), 5064-5087] is proved.

We completely describe the decompositions (into indecomposable submodules) of the tensor products of irreducible sl(2)-modules in characteristic 3. The answer resembles analogous decompositions for the Lie superalgebra sl(1|1).

The character formula of any finite dimensional irreducible module Lλ for Lie superalgebra osp(n|2) is computed. As a by-product, the decomposition of tensor module Lλ ⊗ C n|2, where Cn|2 is the natural representation, is obtained.

We give a complete classification of infinite dimensional indecomposable weight modules over the Lie superalgebra sl(2/1). §1. Introduction Among the basic-classical Lie superalgebras classified by Kac [3], the lowest dimensional of these is the Lie superalgebra B(0, 1) or osp(1, 2), while the lowest dimensional of these which has an isotropic odd simple root is the Lie superalgebra A(1, 0) or ...