A Laplace-Dunkl Equation on S2 and the Bannai–Ito Algebra

@article{Genest2015ALE,
  title={A Laplace-Dunkl Equation on S2 and the Bannai–Ito Algebra},
  author={Vincent X. Genest and Luc Vinet and Alexei S. Zhedanov},
  journal={Communications in Mathematical Physics},
  year={2015},
  volume={336},
  pages={243-259}
}
The analysis of the $${\mathbb{Z}_2^{3}}$$Z23 Laplace-Dunkl equation on the 2-sphere is cast in the framework of the Racah problem for the Hopf algebra sl−1(2). The related Dunkl-Laplace operator is shown to correspond to a quadratic expression in the total Casimir operator of the tensor product of three irreducible sl−1(2)-modules. The operators commuting with the Dunkl Laplacian are seen to coincide with the intermediate Casimir operators and to realize a central extension of the Bannai–Ito… 
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