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Generating function for the Bannai-Ito polynomials


Authors: Geoffroy Bergeron, Luc Vinet and Satoshi Tsujimoto
Journal: Proc. Amer. Math. Soc. 146 (2018), 5077-5090
MSC (2010): Primary 20C35, 33C45, 81R05
DOI: https://doi.org/10.1090/proc/14158
Published electronically: September 10, 2018
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Abstract: A generating function for the Bannai-Ito polynomials is derived using the fact that these polynomials are known to be essentially the Racah or $ 6j$ coefficients of the $ \mathfrak{osp}(1\vert 2)$ Lie superalgebra. The derivation is carried in a realization of the recoupling problem in terms of three Dunkl oscillators.


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Additional Information

Geoffroy Bergeron
Affiliation: Centre de recherches mathématiques, Université de Montréal, P.O. Box 6128, Centre-ville Station, Montréal, H3C 3J7 Canada
Email: bergerog@crm.umontreal.ca

Luc Vinet
Affiliation: Centre de recherches mathématiques, Université de Montréal, P.O. Box 6128, Centre-ville Station, Montréal, H3C 3J7 Canada

Satoshi Tsujimoto
Affiliation: Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, 606-8501, Japan

DOI: https://doi.org/10.1090/proc/14158
Received by editor(s): January 18, 2018
Received by editor(s) in revised form: March 12, 2018
Published electronically: September 10, 2018
Additional Notes: The research of the first author was supported by scholarships of the Natural Science and Engineering Research Council of Canada (NSERC) and of the Fond de Recherche du Québec - Nature et Technologies (FRQNT). The research of the second author was supported in part by a Discovery Grant from NSERC
Communicated by: Mourad Ismail
Article copyright: © Copyright 2018 American Mathematical Society

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