REPRESENTATIONS OF N = 1 EXTENDED SUPERCONFORMAL ALGEBRAS WITH 2 GENERATORS

In this paper we consider the representation theory of N = 1 Super-W-a lgebras with two generators for conformal dimension of the additional superprimary field between two and six. hi the superminimal case our r esults coincide with the expectation from the ADE-classification. For the parabolic algebras we find a finite number of highest weight repre sentations and an effective central charge c = 2/3. Furthermore we sho w that most of the exceptional algebras lead to new rational models wi th c > 3/2. The remaining exceptional cases show a new 'mixed' structu re. Besides a continuous branch of representations discrete values of the highest weight also exist.