Journal of Lie Theory
Vol. 9, No. 1, pp. 69-112 (1999)

Foncteurs de Zuckerman pour les super algebres de Lie

C. Santos

Departamento de Matematica Pura
Faculdade de Ciencias
Praca Gomes Teixeira
4050 Porto

Abstract: Let ${ \frak{g}}$ be a basic classical Lie superalgebra. The aim of this article is the study of certain ${ \frak{g}}$-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 ${ \frak{h}}$ of ${ \frak{g}}$ by ${ H\mapsto{ str}(\rho(H^m))}$, where ${ m\in{\Bbb N}}$ and ${ \rho}$ is a finite-dimensional representation of ${ \frak{g}}$, contains all polynomials functions invariant under the Weyl group which are multiples of every isotropic root.

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