Generalized supersymmetry on Riemann surfaces and the associated string models

The authors propose a generalization of the concept of supersymmetry non Riemann surfaces. Generators of this symmetry intermix M fields of different spin. Two types of statistics, i.e., bosonic and fermionic statistics, are allowed for parameters of infinitesimal transformations. They also study the possibility of string models associated with these symmetries. The algebraic structure of a part of generalized supersymmetry is regarded as a sort of an M-th root of the Virasoro algebra