A two-dimensional superintegrable system of singular oscillators with internal degrees of freedom is identified and exactly solved. Its symmetry algebra is seen to be the dual $-1$ Hahn algebra which describes the bispectral properties of the polynomials with the same name that are essentially the Clebsch-Gordan coefficients of the superconformal algebra $\mathfrak{osp}(1|2)$. It is also shown how this superintegrable model is obtained under dimensional reduction from a set of uncoupled harmonic oscillators in four dimensions.

中文翻译：

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超共形量子力学中的超可积性和对偶−1 Hahn 代数

识别并精确求解了具有内部自由度的奇异振荡器的二维超可积系统。它的对称代数被看作是对偶 $-1$ Hahn 代数，它描述了同名多项式的双谱性质，这些多项式本质上是超共形代数 $\mathfrak{osp}(1|2) 的 Clebsch-Gordan 系数$. 还展示了这个超可积模型是如何从一组四维非耦合谐振子降维的情况下获得的。