The Racah algebra and its higher rank extension are the algebras underlying the univariate and multivariate Racah polynomials. In this paper, we develop two new models in which the Racah algebra naturally arises as symmetry algebra, namely, the Bargmann model and the Barut-Girardello model. We show how both models are connected with the superintegrable model of Miller et al. The Bargmann model moreover leads to a new realization of the Racah algebra of rank n as n-variable differential operators. Our conceptual approach also allows us to rederive the basis functions of the superintegrable model without resorting to separation of variables.
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Research Article| January 23 2019
Bargmann and Barut-Girardello models for the Racah algebra
Hendrik De Bie ;
Hendrik De Bie, Plamen Iliev, Luc Vinet; Bargmann and Barut-Girardello models for the Racah algebra. J. Math. Phys. 1 January 2019; 60 (1): 011701. https://doi.org/10.1063/1.5080985
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