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

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.

9 pages

References in corpus (3)

• Two-Variable Wilson Polynomials and the Generic Superintegrable System on the 3-Sphere
• Embeddings of the Racah Algebra into the Bannai-Ito Algebra
• Bannai-Ito algebras and the $osp(1,2)$ superalgebra

Cited by in corpus (11)

• Fourth order Superintegrable systems separating in Cartesian coordinates I. Exotic quantum potentials
• Quantum superintegrable system with a novel chain structure of quadratic algebras
• The higher rank $q$-deformed Bannai-Ito and Askey-Wilson algebra
• Superintegrability on the Dunkl oscillator model in three-Dimensional spaces of constant curvature
• Higher Rank Relations for the Askey-Wilson and $q$-Bannai-Ito Algebra
• Higher Order Quantum Superintegrability: a new "Painlevé conjecture"
• The $q$-Bannai-Ito algebra and multivariate $(-q)$-Racah and Bannai-Ito polynomials
• The dual pair $Pin(2n)\times \mathfrak{osp}(1|2)$, the Dirac equation and the Bannai-Ito algebra
• Invariant prolongation of the Killing tensor equation
• Higher order superintegrability, Painlevé transcendents and representations of polynomial algebras
• Bivariate Bannai-Ito polynomials