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This article is cited in 13 scientific papers (total in 13 papers)
Embeddings of the Racah Algebra into the Bannai–Ito Algebra
Vincent X. Genest, Luc Vinet, Alexei Zhedanov Centre de Recherches Mathématiques, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal, QC, Canada, H3C 3J7
Abstract:
Embeddings of the Racah algebra into the Bannai–Ito algebra are proposed in two realizations. First, quadratic combinations of the Bannai–Ito algebra generators in their standard realization on the space of polynomials are seen to generate a central extension of the Racah algebra. The result is also seen to hold independently of the realization. Second, the relationship between the realizations of the Bannai–Ito and Racah algebras by the intermediate Casimir operators of the $\mathfrak{osp}(1|2)$ and $\mathfrak{su}(1,1)$ Racah problems is established. Equivalently, this gives an embedding of the invariance algebra of the generic superintegrable system on the two-sphere into the invariance algebra of its extension with reflections, which are respectively isomorphic to the Racah and Bannai–Ito algebras.
Keywords:
Bannai–Ito polynomials; Bannai–Ito algebra; Racah polynomials; Racah algebra.
Received: April 2, 2015; in final form June 25, 2015; Published online June 30, 2015
Citation:
Vincent X. Genest, Luc Vinet, Alexei Zhedanov, “Embeddings of the Racah Algebra into the Bannai–Ito Algebra”, SIGMA, 11 (2015), 050, 11 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1031 https://www.mathnet.ru/eng/sigma/v11/p50
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