**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

Portugal

jcsantos@fc.up.pt

**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.

**Full text of the article:**

[Previous Article] [Next Article] [Contents of this Number]