# The Bannai-Ito polynomials as Racah coefficients of the sl_{-1}(2) algebra

```@article{Genest2012TheBP,
title={The Bannai-Ito polynomials as Racah coefficients of the sl\_\{-1\}(2) algebra},
author={Vincent X. Genest and Luc Vinet and Alexei S. Zhedanov},
journal={arXiv: Mathematical Physics},
year={2012}
}```
• Published 18 May 2012
• Mathematics, Physics
• arXiv: Mathematical Physics
The Bannai-Ito polynomials are shown to arise as Racah coefficients for sl_{-1}(2). This Hopf algebra has four generators including an involution and is defined with both commutation and anticommutation relations. It is also equivalent to the parabosonic oscillator algebra. The coproduct is used to show that the Bannai-Ito algebra acts as the hidden symmetry algebra of the Racah problem for sl_{-1}(2). The Racah coefficients are recovered from a related Leonard pair.
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