The higher rank qdeformed BannaiIto and AskeyWilson algebra
 Author
 Hendrik De Bie (UGent) , Hadewijch De Clercq (UGent) and Wouter van de Vijver (UGent)
 Organization
 Abstract
 The qdeformed BannaiIto 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 AskeyWilson algebra. In the present paper these results will be extended to higher rank. The rank n  2 qBannaiIto algebra A(n)(q), which by the established isomorphism also yields a higher rank version of the AskeyWilson algebra, is constructed in the nfold tensor product of osp(q) (1  2). An explicit realization in terms of qshift operators and reflections is proposed, which will be called the Z(2)(n) qDiracDunkl model. The algebra A(n)(q) is shown to arise as the symmetry algebra of the constructed Z(2)(n) qDiracDunkl operator and to act irreducibly on modules of its polynomial nullsolutions. An explicit basis for these modules is obtained using a qdeformed CKextension and Fischer decomposition.
 Keywords
 DIFFERENCEOPERATORS, POLYNOMIALS, SYSTEMS
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU8663790
 MLA
 De Bie, Hendrik, et al. “The Higher Rank QDeformed BannaiIto and AskeyWilson Algebra.” COMMUNICATIONS IN MATHEMATICAL PHYSICS, vol. 374, no. 1, 2020, pp. 277–316, doi:10.1007/s0022001903562w.
 APA
 De Bie, H., De Clercq, H., & van de Vijver, W. (2020). The higher rank qdeformed BannaiIto and AskeyWilson algebra. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 374(1), 277–316. https://doi.org/10.1007/s0022001903562w
 Chicago authordate
 De Bie, Hendrik, Hadewijch De Clercq, and Wouter van de Vijver. 2020. “The Higher Rank QDeformed BannaiIto and AskeyWilson Algebra.” COMMUNICATIONS IN MATHEMATICAL PHYSICS 374 (1): 277–316. https://doi.org/10.1007/s0022001903562w.
 Chicago authordate (all authors)
 De Bie, Hendrik, Hadewijch De Clercq, and Wouter van de Vijver. 2020. “The Higher Rank QDeformed BannaiIto and AskeyWilson Algebra.” COMMUNICATIONS IN MATHEMATICAL PHYSICS 374 (1): 277–316. doi:10.1007/s0022001903562w.
 Vancouver
 1.De Bie H, De Clercq H, van de Vijver W. The higher rank qdeformed BannaiIto and AskeyWilson 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 qdeformed BannaiIto and AskeyWilson algebra,” COMMUNICATIONS IN MATHEMATICAL PHYSICS, vol. 374, no. 1, pp. 277–316, 2020.
@article{8663790, abstract = {The qdeformed BannaiIto 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 AskeyWilson algebra. In the present paper these results will be extended to higher rank. The rank n  2 qBannaiIto algebra A(n)(q), which by the established isomorphism also yields a higher rank version of the AskeyWilson algebra, is constructed in the nfold tensor product of osp(q) (1  2). An explicit realization in terms of qshift operators and reflections is proposed, which will be called the Z(2)(n) qDiracDunkl model. The algebra A(n)(q) is shown to arise as the symmetry algebra of the constructed Z(2)(n) qDiracDunkl operator and to act irreducibly on modules of its polynomial nullsolutions. An explicit basis for these modules is obtained using a qdeformed CKextension and Fischer decomposition.}, author = {De Bie, Hendrik and De Clercq, Hadewijch and van de Vijver, Wouter}, issn = {00103616}, journal = {COMMUNICATIONS IN MATHEMATICAL PHYSICS}, keywords = {DIFFERENCEOPERATORS,POLYNOMIALS,SYSTEMS}, language = {eng}, number = {1}, pages = {277316}, title = {The higher rank qdeformed BannaiIto and AskeyWilson algebra}, url = {http://dx.doi.org/10.1007/s0022001903562w}, volume = {374}, year = {2020}, }
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