FUSION ALGEBRAS INDUCED BY REPRESENTATIONS OF THE MODULAR GROUP

Using the representation theory of the subgroups SL2 (Z(p)) of the mod ular group we investigate the induced fusion algebras in some simple e xamples. Only some of these representations lead to ''good'' fusion al gebras. Furthermore, the conformal dimensions and the central charge o f the corresponding rational conformal field theories are calculated. Two series of representations which can be realized by unitary theorie s are presented. We show that mort of the fusion algebras induced by a dmissible representations are realized in well-known rational models.