Existence of different intermediate Hamiltonians in type A image-fold supersymmetry II: The image= 3 case Original Research Article

We continue the previous study on the existence of different intermediate Hamiltonians in type A image-fold supersymmetric systems and carry out an exhaustive investigation on the image = 3 case. In contrast with the image = 2 case, we find various patterns in the existence of intermediate Hamiltonians due to the presence of two different intermediate positions in a factorized type A 3-fold supercharge. In addition, all the image = 3 models are strictly restricted to at most elliptic type, which enables us to make the complete classification of the systems which admit intermediate Hamiltonians. Finally, we show realizations of third-order parasupersymmetry and variant generalized 3-fold superalgebras by such systems.