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A superintegrable model with reflections on $S^3$ and the rank two Bannai-Ito algebra
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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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Higher Rank Relations for the Askey-Wilson and $q$-Bannai-Ito Algebra
New commutation and q-commutation relations are proven for generators of the higher rank Askey-Wilson and q-Bannai-Ito algebras, extending the rank-one defining relations.
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