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.

Chevalley’s theorem states that for any simple finite dimensional Lie algebra g: (1) the restriction homomorphism of the algebra of polynomials S(g∗) −→ S(h∗) onto the Cartan subalgebra h induces an isomorphism S(g∗)g ∼= S(h∗)W , where W is the Weyl group of g; (2) each g-invariant polynomial is a linear combination of the polynomials trρ(x)k , where ρ is a finite dimensional representation of ...

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.