A Dirac–Dunkl Equation on S[superscript 2] and the Bannai–Ito Algebra
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A Dirac–Dunkl Equation on S2 and the Bannai–Ito Algebra
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The Dirac–Dunkl operator on the two-sphere associated to the Z[superscript 3][subscript 2] 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.
Date issued
2016-05Department
Massachusetts Institute of Technology. Department of MathematicsJournal
Communications in Mathematical Physics
Publisher
Springer Berlin Heidelberg
Citation
De Bie, Hendrik, Vincent X. Genest, and Luc Vinet. “A Dirac–Dunkl Equation on S 2 and the Bannai–Ito Algebra.” Communications in Mathematical Physics 344, no. 2 (May 9, 2016): 447–464.
Version: Author's final manuscript
ISSN
0010-3616
1432-0916