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The higher rank q-deformed Bannai-Ito and Askey-Wilson algebra

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Abstract
The q-deformed Bannai-Ito algebra was recently constructed in the threefold tensor product of the quantum superalgebra osp(q) (1 | 2). It turned out to be isomorphic to the Askey-Wilson algebra. In the present paper these results will be extended to higher rank. The rank n - 2 q-Bannai-Ito algebra A(n)(q), which by the established isomorphism also yields a higher rank version of the Askey-Wilson algebra, is constructed in the n-fold tensor product of osp(q) (1 | 2). An explicit realization in terms of q-shift operators and reflections is proposed, which will be called the Z(2)(n) q-Dirac-Dunkl model. The algebra A(n)(q) is shown to arise as the symmetry algebra of the constructed Z(2)(n) q-Dirac-Dunkl operator and to act irreducibly on modules of its polynomial null-solutions. An explicit basis for these modules is obtained using a q-deformed CK-extension and Fischer decomposition.
Keywords
DIFFERENCE-OPERATORS, POLYNOMIALS, SYSTEMS

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MLA
De Bie, Hendrik, et al. “The Higher Rank Q-Deformed Bannai-Ito and Askey-Wilson Algebra.” COMMUNICATIONS IN MATHEMATICAL PHYSICS, vol. 374, no. 1, 2020, pp. 277–316, doi:10.1007/s00220-019-03562-w.
APA
De Bie, H., De Clercq, H., & van de Vijver, W. (2020). The higher rank q-deformed Bannai-Ito and Askey-Wilson algebra. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 374(1), 277–316. https://doi.org/10.1007/s00220-019-03562-w
Chicago author-date
De Bie, Hendrik, Hadewijch De Clercq, and Wouter van de Vijver. 2020. “The Higher Rank Q-Deformed Bannai-Ito and Askey-Wilson Algebra.” COMMUNICATIONS IN MATHEMATICAL PHYSICS 374 (1): 277–316. https://doi.org/10.1007/s00220-019-03562-w.
Chicago author-date (all authors)
De Bie, Hendrik, Hadewijch De Clercq, and Wouter van de Vijver. 2020. “The Higher Rank Q-Deformed Bannai-Ito and Askey-Wilson Algebra.” COMMUNICATIONS IN MATHEMATICAL PHYSICS 374 (1): 277–316. doi:10.1007/s00220-019-03562-w.
Vancouver
1.
De Bie H, De Clercq H, van de Vijver W. The higher rank q-deformed Bannai-Ito and Askey-Wilson algebra. COMMUNICATIONS IN MATHEMATICAL PHYSICS. 2020;374(1):277–316.
IEEE
[1]
H. De Bie, H. De Clercq, and W. van de Vijver, “The higher rank q-deformed Bannai-Ito and Askey-Wilson algebra,” COMMUNICATIONS IN MATHEMATICAL PHYSICS, vol. 374, no. 1, pp. 277–316, 2020.
@article{8663790,
  abstract     = {The q-deformed Bannai-Ito algebra was recently constructed in the threefold tensor product of the quantum superalgebra osp(q) (1 | 2). It turned out to be isomorphic to the Askey-Wilson algebra. In the present paper these results will be extended to higher rank. The rank n - 2 q-Bannai-Ito algebra A(n)(q), which by the established isomorphism also yields a higher rank version of the Askey-Wilson algebra, is constructed in the n-fold tensor product of osp(q) (1 | 2). An explicit realization in terms of q-shift operators and reflections is proposed, which will be called the Z(2)(n) q-Dirac-Dunkl model. The algebra A(n)(q) is shown to arise as the symmetry algebra of the constructed Z(2)(n) q-Dirac-Dunkl operator and to act irreducibly on modules of its polynomial null-solutions. An explicit basis for these modules is obtained using a q-deformed CK-extension and Fischer decomposition.},
  author       = {De Bie, Hendrik and De Clercq, Hadewijch and van de Vijver, Wouter},
  issn         = {0010-3616},
  journal      = {COMMUNICATIONS IN MATHEMATICAL PHYSICS},
  keywords     = {DIFFERENCE-OPERATORS,POLYNOMIALS,SYSTEMS},
  language     = {eng},
  number       = {1},
  pages        = {277--316},
  title        = {The higher rank q-deformed Bannai-Ito and Askey-Wilson algebra},
  url          = {http://dx.doi.org/10.1007/s00220-019-03562-w},
  volume       = {374},
  year         = {2020},
}

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