Let g be a basic classical Lie superalgebra. The aim of this article is the study of certain g-modules obtained by a method called homological induction. It is proved that the finite-dimensional typical modules can be obtained in this way and the Weyl-Kac character formula is deduced. It is also proved that the vector space spanned by the polynomial functions defined on a Cartan subalgebra h of g by H --> str(p(H-m)), where m epsilon N and rho is a finite-dimensional representation of g, contains all polynomials functions invariant under the Weyl group which are multiples of every isotropic root.
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