Fusion rules and singular vectors of the osp (12) current algebra Original Research Article

The fusion of Verma modules of the osp (12) current algebra is studied. In the framework of an isotopic formalism, the singular vector decoupling conditions are analyzed. The fusion rules corresponding to the admissible representations of the osp12) algebra are determined. A relation between the characters of these last representations and those corresponding to the minimal superconformal models is found. A series of equations that relate the descendants of the highest weight vectors resulting from a fusion of Verma modules are obtained. Solving these equations the singular vectors of the theory can be determined.