CLASSIFICATION OF HARISH-CHANDRA MODULES OVER THE SUPER-VIRASORO ALGEBRAS

In this paper, we first construct all indecomposable modules whose dim ensions of weight spaces of the even and odd parts are less than or eq ual to 1, then classify all Harish-Chandra module over the super-Viras oro algebras, proving that every Harish-Chandra module over the super- Virasoro algebras is either a highest or lowest weight module, or else a module of the intermediate series. This result generalizes a theore m which was originally given as a conjecture by Kac on the Virasoro al gebra.