A superintegrable model with reflections on Sn−1 and the higher rank Bannai–Ito algebra

Abstract

A quantum superintegrable model with reflections on the (n − 1)-sphere is presented. Its symmetry algebra is identified with the higher rank generalization of the Bannai–Ito algebra. It is shown that the Hamiltonian of the system can be constructed from the tensor product of n representations of the superalgebra and that the superintegrability is naturally understood in that setting. The separated solutions are obtained through the Fischer decomposition and a Cauchy–Kovalevskaia extension theorem.