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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.

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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