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Transactions of the American Mathematical Society

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


Authors: Vincent X. Genest, Luc Lapointe and Luc Vinet
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 17B37; Secondary 81R05
DOI: https://doi.org/10.1090/tran/7733
Published electronically: December 7, 2018
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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$.


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Additional Information

Vincent X. Genest
Affiliation: Department of Mathematics, Massachussetts Institute of Technology, Cambridge, Massachusetts 02139
Email: vxgenest@mit.edu

Luc Lapointe
Affiliation: Instituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca, Chile
Email: lapointe@inst-mat.utalca.cl

Luc Vinet
Affiliation: Centre de Recherches Mathématiques, Université de Montréal, Montréal, Québec H3C 3J7, Canada
Email: luc.vinet@umontreal.ca

DOI: https://doi.org/10.1090/tran/7733
Keywords: Bannai--Ito algebra
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.
Article copyright: © Copyright 2018 American Mathematical Society