Kac–Moody superalgebras and integrability

Abstract

The first part of this paper is a review and systematization of known results on (infinite-dimensional) contragredient Lie superalgebras and their representations. In the second part, we obtain character formulae for integrable highest weight representations of sl (1|n) and osp (2|2n); these formulae were conjectured by Kac–Wakimoto.