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arXiv · 1601.07642

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

Hendrik De Bie·Vincent X. Genest·Jean-Michel Lemay·Luc Vinet
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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.

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Hendrik De Bie, Vincent X. Genest, Jean-Michel Lemay, Luc Vinet. 2016-01-28. A superintegrable model with reflections on $S^3$ and the rank two Bannai-Ito algebra. https://arxiv.org/abs/1601.07642

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