## $\mathfrak {osp}(1,2)$ and generalized Bannai–Ito algebras

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- by Vincent X. Genest, Luc Lapointe and Luc Vinet PDF
- Trans. Amer. Math. Soc.
**372**(2019), 4127-4148 Request permission

## Abstract:

Generalizations of the (rank-$1$) Bannai–Ito algebra are obtained from a refinement of the grade involution of the Lie superalgebra $\mathfrak {osp}(1,2)$. A hyperoctahedral extension is derived by using a realization of $\mathfrak {osp}(1,2)$ in terms of Dunkl operators associated with the Weyl group $B_3$.## References

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## Additional Information

**Vincent X. Genest**- Affiliation: Department of Mathematics, Massachussetts Institute of Technology, Cambridge, Massachusetts 02139
- MR Author ID: 970414
- Email: vxgenest@mit.edu
**Luc Lapointe**- Affiliation: Instituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca, Chile
- MR Author ID: 340905
- Email: lapointe@inst-mat.utalca.cl
**Luc Vinet**- Affiliation: Centre de Recherches Mathématiques, Université de Montréal, Montréal, Québec H3C 3J7, Canada
- MR Author ID: 178665
- ORCID: 0000-0001-6211-7907
- Email: luc.vinet@umontreal.ca
- Received by editor(s): May 26, 2017
- Received by editor(s) in revised form: August 5, 2018
- Published electronically: December 7, 2018
- Additional Notes: The first author holds a postdoctoral fellowship from the Natural Science and Engineering Research Council (NSERC) of Canada.

The research of the second author is supported by Fondo Nacional de Desarrollo Científico y Tecnológico (FONDECYT) de Chile grant #1170924.

The third author gratefully acknowledges his support from NSERC through a discovery grant. - © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**372**(2019), 4127-4148 - MSC (2010): Primary NUMBER(S)
- DOI: https://doi.org/10.1090/tran/7733
- MathSciNet review: 4009427