论文标题
RACAH代数：概述和最新结果
The Racah algebra: An overview and recent results
论文作者
论文摘要
审查了RACAH代数$ \ Mathcal {R} _n $等级$ n -2 $的最新结果。 $ \ mathcal {r} _n $是根据生成器和关系定义的，并且位于$ \ mathfrak {su}（1,1）$的对角线中的中央器中，$ \ mathcal {u}（\ mathfrak {\ mathfrak）讨论了它与多元RACAH多项式的联系。它被证明是$（n -1）$ - 球体上通用整合模型的对称代数，并提供了许多有趣的实现。
Recent results on the Racah algebra $\mathcal{R}_n$ of rank $n - 2$ are reviewed. $\mathcal{R}_n$ is defined in terms of generators and relations and sits in the centralizer of the diagonal action of $\mathfrak{su}(1,1)$ in $\mathcal{U}(\mathfrak{su}(1,1))^{\otimes n}$. Its connections with multivariate Racah polynomials are discussed. It is shown to be the symmetry algebra of the generic superintegrable model on the $ (n-1)$ - sphere and a number of interesting realizations are provided.
