A superintegrable model with reflections on $S^{n-1}$ and the higher rank Bannai-Ito algebra

TL;DR

This paper introduces a quantum superintegrable model with reflections on the sphere, revealing its symmetry algebra as a higher rank Bannai-Ito algebra and demonstrating its construction from tensor products of superalgebra representations.

Contribution

It presents a new superintegrable model on the sphere with a symmetry algebra as a higher rank Bannai-Ito algebra, constructed via tensor products of rak{osp}(1|2) representations.

Findings

The model's symmetry algebra is identified as a higher rank Bannai-Ito algebra.

The Hamiltonian is constructed from tensor products of rak{osp}(1|2) representations.

Separated solutions are obtained through Fischer decomposition and Cauchy-Kovalevskaia extension.

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 $\mathfrak{osp}(1|2)$ 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.