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Symmetry, Integrability and Geometry: Methods and Applications, 2015, Volume 11, 057, 17 pp.
DOI: https://doi.org/10.3842/SIGMA.2015.057
(Mi sigma1038)
 

This article is cited in 16 scientific papers (total in 16 papers)

Racah Polynomials and Recoupling Schemes of $\mathfrak{su}(1,1)$

Sarah Post

Department of Mathematics, University of Hawai‘i at Mānoa, Honolulu, HI, 96822, USA
References:
Abstract: The connection between the recoupling scheme of four copies of $\mathfrak{su}(1,1)$, the generic superintegrable system on the 3 sphere, and bivariate Racah polynomials is identified. The Racah polynomials are presented as connection coefficients between eigenfunctions separated in different spherical coordinate systems and equivalently as different irreducible decompositions of the tensor product representations. As a consequence of the model, an extension of the quadratic algebra ${\rm QR}(3)$ is given. It is shown that this algebra closes only with the inclusion of an additional shift operator, beyond the eigenvalue operators for the bivariate Racah polynomials, whose polynomial eigenfunctions are determined. The duality between the variables and the degrees, and hence the bispectrality of the polynomials, is interpreted in terms of expansion coefficients of the separated solutions.
Keywords: orthogonal polynomials; Lie algebras; representation theory.
Received: April 16, 2015; in final form July 14, 2015; Published online July 23, 2015
Bibliographic databases:
Document Type: Article
Language: English
Citation: Sarah Post, “Racah Polynomials and Recoupling Schemes of $\mathfrak{su}(1,1)$”, SIGMA, 11 (2015), 057, 17 pp.
Citation in format AMSBIB
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  • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
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