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 $\mathfrak{ osp}(1|2)$ 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.
Categories: math-ph math.MP