Existence of different intermediate Hamiltonians in type A image-fold supersymmetry Original Research Article

Type A image-fold supercharge admits a one-parameter family of factorizations into product of image first-order linear differential operators due to an underlying image symmetry. As a consequence, a type A image-fold supersymmetric system can have different intermediate Hamiltonians corresponding to different factorizations. We derive the necessary and sufficient conditions for the latter system to possess intermediate Hamiltonians for the image case. We then show that whenever it has (at least) one intermediate Hamiltonian, it can admit second-order parasupersymmetry and a generalized 2-fold superalgebra. As an illustration, we construct a set of generalized Pöschl–Teller potentials of this kind.