Association schemes and quadratic transformations for orthogonal polynomials

Laura Chihara, Dennis Stanton

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)101-112
Number of pages12
JournalGraphs and Combinatorics
Issue number1
StatePublished - Dec 1986


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