Abstract
Special cases of the Askey-Wilson polynomials are the eigenmatrices of the classical association schemes. Three constructions on the schemes — multiple polynomial structures, bipartite halves, and antipodal quotients — give quadratic transformations for the polynomials. It is shown that these transformations essentially follow from a quadratic transformation for the Askey-Wilson polynomials. Explicit formulas for the eigenmatrices of three related association schemes are given.
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Partially supported by NSF grant DMS: 8500958 and a fellowship from the Sloan Foundation.
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Chihara, L., Stanton, D. Association schemes and quadratic transformations for orthogonal polynomials. Graphs and Combinatorics 2, 101–112 (1986). https://doi.org/10.1007/BF01788084
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DOI: https://doi.org/10.1007/BF01788084