The Bannai-Ito algebra and some applications
Hendrik De Bie, Vincent X. Genest, Satoshi Tsujimoto, Luc Vinet and, Alexei Zhedanov
TL;DR
This paper explores the Bannai-Ito algebra, detailing its connections to special polynomials, algebraic problems, superintegrable systems, and differential equations, highlighting its broad mathematical and physical applications.
Contribution
It provides a comprehensive survey of the Bannai-Ito algebra and its diverse applications across multiple areas of mathematical physics.
Findings
Relations with Bannai-Ito polynomials elucidated
Connections to the Racah problem for $sl_{-1}(2)$ established
Applications to superintegrable models and Dirac-Dunkl equations discussed
Abstract
The Bannai-Ito algebra is presented together with some of its applications. Its relations with the Bannai-Ito polynomials, the Racah problem for the algebra, a superintegrable model with reflections and a Dirac-Dunkl equation on the 2-sphere are surveyed.
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