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arXiv · 2604.26122

The dynamical algebra of the generic superintegrable model on the two-sphere

Nicolas Crampé·Quentin Labriet·Lucia Morey·Satoshi Tsujimoto·Luc Vinet·Alexei Zhedanov
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Abstract

The rank two Jacobi algebra $\mathfrak{J}_2$ is identified as the dynamical algebra of the generic quadratic superintegrable model on the two-sphere. The physical representation of this algebra is obtained from its embedding in $\mathfrak{su}(1,1)^{\otimes 3}$. The exact solution of the model is derived algebraically from this representation. The wavefunctions are found to be expressed in terms of two-variable Jacobi polynomials whose characterization is a by-product of the algebraic treatment of the model.

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Nicolas Crampé, Quentin Labriet, Lucia Morey, Satoshi Tsujimoto, Luc Vinet, Alexei Zhedanov. 2026-04-28. The dynamical algebra of the generic superintegrable model on the two-sphere. https://arxiv.org/abs/2604.26122

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