A Laplace-Dunkl equation on $S^2$ and the Bannai-Ito algebra

Vincent X. Genest, Luc Vinet, Alexei Zhedanov

The analysis of the ${\mathbb{Z}}_2^3$ Laplace-Dunkl equation on the $2$-sphere is cast in the framework of the Racah problem for the Hopf algebra $s{l}_{-1}(2)$. The related Dunkl-L…