Contravariant form for infinite-dimensional Lie algebras and superalgebras

In this article a criterion of irreducibility of a representation with vacuum vector of the Lie superalgebras of (A,tau) and of the string algebra and superalgebra (Virasoro and Neveu-Schwartz models) is found. The method consists in the computation of the determinant of the so-called contravariant form. As a consequence we obtain a description of the composition series of the representation with vacuum vector and formular for the characters of some irreducible representations with vacuum vector. (orig./HSI)