FUSION RULES AND SINGULAR VECTORS OF THE OSP(1 2) CURRENT-ALGEBRA/

The fusion of Verma modules of the osp(1/2) current algebra is studied . In the framework of an isotopic formalism, the singular vector decou pling conditions are analyzed. The fusion rules corresponding to the a dmissible representations of the osp(1/2) algebra are determined. A re lation 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. (C) 19 97 Elsevier Science B.V.