The equitable Racah algebra from three su(1,1) algebras

Abstract

The Racah algebra, a quadratic algebra with two independent generators, is central in the analysis of superintegrable models and encodes the properties of the Racah polynomials. It is the algebraic structure behind the su(1,1) Racah problem as it is realized by the intermediate Casimir operators arising in the addition of three irreducible su(1,1) representations. It has been shown that this Racah algebra can also be obtained from quadratic elements in the enveloping algebra of su(2). The correspondence between these two realizations is here explained and made explicit.

11 pages; Minor changes

Cited by in corpus (22)

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• Embeddings of the Racah Algebra into the Bannai-Ito Algebra
• Finite-Dimensional Irreducible Modules of the Racah Algebra at Characteristic Zero
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• Algebraic (super-)integrability from commutants of subalgebras in universal enveloping algebras
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• Superspace realizations of the Bannai-Ito algebra
• Matrix elements of $SO(3)$ in $s{l}_3$ representations as bispectral multivariate functions