Representations of Lie Superalgebras an Introduction

Abstract

An introductory overview over the theory of finite-dimensional representations of a Lie superalgebra is given. The most basic constructions with the representations of a Lie superalgebra are described, the enveloping algebra is introduced, and the induced representations are defined and then investigated for a special class of consistently Z — graded Lie superalgebras. On the example of the general linear Lie superalgebras the classical theory of roots and weights is generalized to the super case and it is shown how one is led to the so-called typical representations. Finally, the decomposition of the tensorial powers of a representation by means of the action of the symmetric group is briefly discussed.