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

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 finitedimensional restriction yields a representation that acts on the para-Racah polynomials.

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