The Racah algebra: An overview and recent results
| Autor: | Luc Vinet, Hendrik De Bie, Plamen Iliev, Wouter van de Vijver |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Lie Groups, Number Theory, and Vertex Algebras. :3-20 |
| ISSN: | 1098-3627 0271-4132 |
| DOI: | 10.1090/conm/768/15450 |
| Popis: | 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. 18 pages, survey paper based on talk at the conference Representation Theory XVI in Dubrovnik, 2019. Version 2: some typos corrected and references updated. Accepted for publication in Contemporary Mathematics |
| Databáze: | OpenAIRE |
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