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

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Abstract
The Dirac–Dunkl operator on the two-sphere 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 finite-dimensional 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

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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 author-date
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 author-date (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 two-sphere 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 finite-dimensional irreducible representations of the Bannai–Ito algebra.},
  author       = {De Bie, Hendrik and Genest, Vincent X and Vinet, Luc},
  issn         = {0010-3616},
  journal      = {COMMUNICATIONS IN MATHEMATICAL PHYSICS},
  keywords     = {REFLECTION GROUPS,Cauchy–Kovalevskaia extension,POLYNOMIALS,OPERATORS,Dirac–Dunkl equation,Bannai–Ito algebra},
  language     = {eng},
  number       = {2},
  pages        = {447--464},
  publisher    = {SPRINGER},
  title        = {A Dirac–Dunkl equation on S^2 and the Bannai–Ito algebra},
  url          = {http://dx.doi.org/10.1007/s00220-016-2648-1},
  volume       = {344},
  year         = {2016},
}

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