A superintegrable model with reflections on $S^3$ and the rank two Bannai-Ito algebra

TL;DR

This paper introduces a quantum superintegrable model on the three-sphere with reflections, revealing its symmetry algebra as the rank-two Bannai-Ito algebra and providing explicit solutions via algebraic methods.

Contribution

It constructs a new superintegrable quantum model on $S^3$ with symmetry algebra identified as the rank-two Bannai-Ito algebra, and derives exact solutions using algebraic decomposition techniques.

Findings

Symmetry algebra is the rank-two Bannai-Ito algebra.

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

Exact separated solutions obtained via Fischer decomposition and Cauchy-Kovalevskaia extension.

Abstract

A quantum superintegrable model with reflections on the three-sphere is presented. Its symmetry algebra is identified with the rank-two Bannai-Ito algebra. It is shown that the Hamiltonian of the system can be constructed from the tensor product of four representations of the superalgebra $\mathfrak{osp}(1|2)$ and that the superintegrability is naturally understood in that setting. The exact separated solutions are obtained through the Fischer decomposition and a Cauchy-Kovalevskaia extension theorem.