We use the technique of Harish-Chandra bimodules to prove that regular strongly typical blocks of the category O for the queer Lie superalgebra qn are equivalent to the corresponding blocks of the category O for the Lie algebra gl n .

We provide formulas for the Weyl-Kac denominator and superdenominator of a basic classical Lie superalgebra for a distinguished set of positive roots. Résumé. Nous donnons les formules pour les dénominateurs et super-dénominateurs de Weyl-Kac d’une superalgèbre de Lie basique classique pour un ensemble distingué de racines positives.

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.