Generating function for the Bannai-Ito polynomials
Author:
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 6 j 6j coefficients of the o s p ( 1 | 2 ) \mathfrak {osp}(1|2) Lie superalgebra. The derivation is carried in a realization of the recoupling problem in terms of three Dunkl oscillators.
Funder
Natural Sciences and Engineering Research Council of Canada
Publisher
American Mathematical Society (AMS)
Subject
Applied Mathematics,General Mathematics
Link
https://www.ams.org/proc/2018-146-12/S0002-9939-2018-14158-1/proc14158_AM.pdf
Reference14 articles.
1. Generating functions for the 𝔬𝔰𝔭(1|2) Clebsch-Gordan coefficients;Bergeron, Geoffroy;J. Phys. A,2016
2. The generic superintegrable system on the 3-sphere and the 9𝑗 symbols of 𝔰𝔲(1,1);Genest, Vincent X.;SIGMA Symmetry Integrability Geom. Methods Appl.,2014
3. A Laplace-Dunkl equation on 𝑆² and the Bannai-Ito algebra;Genest, Vincent X.;Comm. Math. Phys.,2015
4. The Bannai-Ito polynomials as Racah coefficients of the 𝑠𝑙₋₁(2) algebra;Genest, Vincent X.;Proc. Amer. Math. Soc.,2014
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