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arXiv · 2001.11195

The Racah algebra: An overview and recent results

Hendrik De Bie·Plamen Iliev·Wouter van de Vijver·Luc Vinet
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Abstract

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.

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BibTeXRIS

Hendrik De Bie, Plamen Iliev, Wouter van de Vijver, Luc Vinet. 2020-01-30. The Racah algebra: An overview and recent results. https://doi.org/10.1090/conm%2F768%2F15450

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