A Dirac–Dunkl equation on S^2 and the Bannai–Ito algebra
 Author
 Hendrik De Bie (UGent) , Vincent X Genest and Luc Vinet
 Organization
 Abstract
 The Dirac–Dunkl operator on the twosphere associated to the 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 finitedimensional irreducible representations of the Bannai–Ito algebra.
 Keywords
 REFLECTION GROUPS, Cauchy–Kovalevskaia extension, POLYNOMIALS, OPERATORS, Dirac–Dunkl equation, Bannai–Ito algebra
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU8174855
 MLA
 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 344.2 (2016): 447–464. Print.
 APA
 De Bie, H., Genest, V. X., & Vinet, L. (2016). A Dirac–Dunkl equation on S^2 and the Bannai–Ito algebra. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 344(2), 447–464.
 Chicago authordate
 De Bie, Hendrik, Vincent X Genest, and Luc Vinet. 2016. “A Dirac–Dunkl Equation on S^2 and the Bannai–Ito Algebra.” Communications in Mathematical Physics 344 (2): 447–464.
 Chicago authordate (all authors)
 De Bie, Hendrik, Vincent X Genest, and Luc Vinet. 2016. “A Dirac–Dunkl Equation on S^2 and the Bannai–Ito Algebra.” Communications in Mathematical Physics 344 (2): 447–464.
 Vancouver
 1.De Bie H, Genest VX, Vinet L. A Dirac–Dunkl equation on S^2 and the Bannai–Ito algebra. COMMUNICATIONS IN MATHEMATICAL PHYSICS. 233 SPRING ST, NEW YORK, NY 10013: SPRINGER; 2016;344(2):447–64.
 IEEE
 [1]H. De Bie, V. X. Genest, and L. Vinet, “A Dirac–Dunkl equation on S^2 and the Bannai–Ito algebra,” COMMUNICATIONS IN MATHEMATICAL PHYSICS, vol. 344, no. 2, pp. 447–464, 2016.
@article{8174855, abstract = {The Dirac–Dunkl operator on the twosphere associated to the 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 finitedimensional irreducible representations of the Bannai–Ito algebra.}, author = {De Bie, Hendrik and Genest, Vincent X and Vinet, Luc}, issn = {00103616}, journal = {COMMUNICATIONS IN MATHEMATICAL PHYSICS}, keywords = {REFLECTION GROUPS,Cauchy–Kovalevskaia extension,POLYNOMIALS,OPERATORS,Dirac–Dunkl equation,Bannai–Ito algebra}, language = {eng}, number = {2}, pages = {447464}, publisher = {SPRINGER}, title = {A Dirac–Dunkl equation on S^2 and the Bannai–Ito algebra}, url = {http://dx.doi.org/10.1007/s0022001626481}, volume = {344}, year = {2016}, }
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