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

TL;DR

This paper demonstrates that Bannai-Ito polynomials serve as Racah coefficients for the Hopf algebra sl_{-1}(2), revealing their role as hidden symmetries in the Racah problem and connecting them to Leonard pairs.

Contribution

It establishes a novel link between Bannai-Ito polynomials and Racah coefficients of the sl_{-1}(2) algebra, expanding understanding of their algebraic and symmetry properties.

Findings

Bannai-Ito polynomials are Racah coefficients for sl_{-1}(2)

The algebra acts as hidden symmetry in the Racah problem

Racah coefficients are derived from Leonard pairs

Abstract

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.