
Symmetry and Integrability of Equations of Mathematical Physics − 2011
Anatoly Nikitin
(Institute of Mathematics of NAS of Ukraine, Kyiv, Ukraine)
Dual shape invariance and superintegrable models for arbitrary spin
Abstract:
Shape invariant matrix potentials are classified. It is demonstrated that some of such potentials
can be generated by two nonequivalent superpotentials. We call this property
dual shape invariance. Examples of physical models admitting dual shape invariance are
discussed, and they are the superintegrable Pronko models for arbitrary spin. We prove
that, in addition to the dynamical symmetry w.r.t. algebra O(1,2) these models are supersymmetric
and dually shape invariant, and use these properties to construct their exact solutions.

