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arXiv · 1610.02638

A higher rank Racah algebra and the $\mathbb{Z}_2^{n}$ Laplace-Dunkl operator

Hendrik De Bie·Vincent X. Genest·Wouter van de Vijver·Luc Vinet
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Abstract

A higher rank generalization of the (rank one) Racah algebra is obtained as the symmetry algebra of the Laplace-Dunkl operator associated to the $\mathbb{Z}_2^n$ root system. This algebra is also the invariance algebra of the generic superintegrable model on the $n$-sphere. Bases of Dunkl harmonics are constructed explicitly using a Cauchy-Kovalevskaia theorem. These bases consist of joint eigenfunctions of maximal Abelian subalgebras of the higher rank Racah algebra. A method to obtain expressions for both the connection coefficients between these bases and the action of the symmetries on these bases is presented.

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Hendrik De Bie, Vincent X. Genest, Wouter van de Vijver, Luc Vinet. 2018-09-06. A higher rank Racah algebra and the $\mathbb{Z}_2^{n}$ Laplace-Dunkl operator. https://doi.org/10.1088/1751-8121%2Faa9756

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