The Gasper and Rahman multivariate $(-q)$‐Racah polynomials appear as connection coefficients between bases diagonalizing different abelian subalgebras of the recently defined higher rank $q$‐Bannai–Ito algebra ${\mathcal{A}}_n^q$. Lifting the action of the algebra to the connection coefficients, we find a realization of ${\mathcal{A}}_n^q$ by means of difference operators. This provides an algebraic interpretation for the bispectrality of the multivariate $(-q)$‐Racah polynomials, as was established in Iliev (Trans. Amer. Math. Soc. 363(3) (2011) 1577–1598).

中文翻译：

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q-Bannai-Ito代数以及多元（-q）-Racah和Bannai-Ito多项式

Gasper和Rahman多元变量 $（-q）$‐Racah多项式显示为对角化了最近定义的更高秩的不同阿贝尔次代数的基之间的连接系数 $q$‐Bannai–Ito代数 ${\mathcal{一种}}_{ñ}^q$。将代数的作用提升到连接系数，我们发现${\mathcal{一种}}_{ñ}^q$通过差异运算符。这为多元双光谱提供了代数解释$（-q）$-Racah多项式，如成立于伊利耶夫（反式。阿梅尔。数学会志。363（3）（2011）1577年至1598年）。