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Bargmann and Barut-Girardello models for the Racah algebra

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Abstract
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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Mathematical Physics

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Chicago
De Bie, Hendrik, Plamen Iliev, and Luc Vinet. 2019. “Bargmann and Barut-Girardello Models for the Racah Algebra.” Journal of Mathematical Physics 60 (1).
APA
De Bie, H., Iliev, P., & Vinet, L. (2019). Bargmann and Barut-Girardello models for the Racah algebra. JOURNAL OF MATHEMATICAL PHYSICS, 60(1).
Vancouver
1.
De Bie H, Iliev P, Vinet L. Bargmann and Barut-Girardello models for the Racah algebra. JOURNAL OF MATHEMATICAL PHYSICS. AIP Publishing; 2019;60(1).
MLA
De Bie, Hendrik, Plamen Iliev, and Luc Vinet. “Bargmann and Barut-Girardello Models for the Racah Algebra.” JOURNAL OF MATHEMATICAL PHYSICS 60.1 (2019): n. pag. Print.
@article{8603440,
  abstract     = {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.},
  articleno    = {011701},
  author       = {De Bie, Hendrik and Iliev, Plamen and Vinet, Luc},
  issn         = {0022-2488},
  journal      = {JOURNAL OF MATHEMATICAL PHYSICS},
  language     = {eng},
  number       = {1},
  pages        = {13},
  publisher    = {AIP Publishing},
  title        = {Bargmann and Barut-Girardello models for the Racah algebra},
  url          = {http://dx.doi.org/10.1063/1.5080985},
  volume       = {60},
  year         = {2019},
}

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