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arXiv · 1501.03108

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

Hendrik De Bie·Vincent X. Genest·Luc Vinet
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Abstract

The Dirac-Dunkl operator on the 2-sphere associated to the $\mathbb{Z}_2^3$ reflection group is considered. Its symmetries are found and are shown to generate the Bannai-Ito algebra. Representations of the Bannai-Ito algebra are constructed using ladder operators. Eigenfunctions of the spherical Dirac-Dunkl operator are obtained using a Cauchy-Kovalevskaia extension theorem. These eigenfunctions, which correspond to Dunkl monogenics, are seen to support finite-dimensional irreducible representations of the Bannai-Ito algebra.

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Hendrik De Bie, Vincent X. Genest, Luc Vinet. 2015-01-13. A Dirac-Dunkl equation on $S^2$ and the Bannai-Ito algebra. https://doi.org/10.1007/s00220-016-2648-1

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