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

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.

8 pages

References in corpus (5)

• Two-Variable Wilson Polynomials and the Generic Superintegrable System on the 3-Sphere
• Bispectrality of the Complementary Bannai-Ito Polynomials
• A Bochner Theorem for Dunkl Polynomials
• Embeddings of the Racah Algebra into the Bannai-Ito Algebra
• The ${\mathbb{Z}}_2^n$ Dirac-Dunkl operator and a higher rank Bannai-Ito algebra

Cited by in corpus (1)

• Higher Rank Relations for the Askey-Wilson and $q$-Bannai-Ito Algebra