REPRESENTATIONS OF CENTRAL EXTENSIONS OF DIFFERENTIABLY SIMPLE LIE-SUPERALGEBRAS

Let S be a simple Lie algebra of characteristic 0 and LAMBDA(n) be the Grassmann superalgebra in n indeterminates. We can form the Lie superalgebra S x LAMBDA(n). The purpose of this paper is to classify all finite dimensional irreducible representations of all central extensions of S x LAMBDA(n). We will also give a character formula for these representations.