The rational Sklyanin algebra and the Wilson and para-Racah polynomials
Quantum Algebra
2022-06-16 v1 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.2103.09631,
title = {The rational Sklyanin algebra and the Wilson and para-Racah polynomials},
author = {Geoffroy Bergeron and Julien Gaboriaud and Luc Vinet and Alexei Zhedanov},
journal= {arXiv preprint arXiv:2103.09631},
year = {2022}
}
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16 pages