Representations of Lie superalgebras

The finite-dimensional representations of the Lie superalgebras of the series S (1. n). G/(1, n), and OSP(2, 2n) over the field of complex numbers are completely described. The representations are realized in tensor fields on a one-point supermanifold; the most important of these fields are identified and are generalized integral and differential forms. Instanton fiber bundles are associated with these most important fields. It is shown that, in contrast to the theory of Lie algebras, the Laplaee-Casimir operators play a modest role in the theory of representations of Lie superalgebras. Namely, the representations of Lie superalgebras are not completely reducible and different nondecomposable representations can have the same set of eigenvalues of all the Laplace- Casimir operators.