The rational Sklyanin algebra and the Wilson and para-Racah polynomials-Reference-Cited by-同舟云学术

The rational Sklyanin algebra and the Wilson and para-Racah polynomials

Published:2022-06-01 Issue:6 Volume:63 Page:061704
ISSN:0022-2488
Container-title:Journal of Mathematical Physics
language:en
Short-container-title:J. Math. Phys.

Author:

Bergeron Geoffroy¹^ORCID,Gaboriaud Julien¹²^ORCID,Vinet Luc¹^ORCID,Zhedanov Alexei³^ORCID

Affiliation:

1. Centre de recherches Mathématiques, Université de Montréal, P.O. Box 6128, Centre-Ville Station, Montréal, Québec H3C 3J7, Canada

2. Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan

3. School of Mathematics, Renmin University of China, Beijing 100872, China

Abstract

The relation between Wilson and para-Racah polynomials and representations of the degenerate rational Sklyanin algebra is established. Second-order Heun operators on quadratic grids with no diagonal terms are determined. These special or S-Heun operators lead to the rational degeneration of the Sklyanin algebra; they also entail the contiguity and structure operators of the Wilson polynomials. The finite-dimensional restriction yields a representation that acts on the para-Racah polynomials.

Funder

Natural Sciences and Engineering Research Council of Canada

National Science Foundation of China

Publisher

AIP Publishing

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Link

https://aip.scitation.org/doi/pdf/10.1063/5.0050471

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