Abstract
A model of the Bannai–Ito algebra in a superspace is introduced. It is obtained from the threefold tensor product of the basic realization of the Lie superalgebra \(\mathfrak {osp}(1|2)\) in terms of operators in one continuous and one Grassmanian variable. The basis vectors of the resulting Bannai–Ito algebra module involve Jacobi polynomials.
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Acknowledgements
The authors wish to acknowledge the enlightening discussions they had with Wouter van de Vijver in the early stages of the project. The authors also would like to thank the referees for suggestions to improve an earlier version of the paper. NC and PI are grateful to the Centre de Recherches Mathématiques (CRM) for supporting visits during which the research reported here was carried out. NC is funded by the international research project AAPT of the CNRS and the ANR Project AHA ANR-18-CE40-0001. HDB is supported by the EOS-FWO Research Project Grant No. (30889451). PI is supported in part by Simons Foundation Grant No. (#635462). LV is supported in part by a Discovery Grant from NSERC.
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Crampé, N., De Bie, H., Iliev, P. et al. Superspace realizations of the Bannai–Ito algebra. Lett Math Phys 113, 108 (2023). https://doi.org/10.1007/s11005-023-01731-6
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DOI: https://doi.org/10.1007/s11005-023-01731-6