Graphs and Combinatorics

, Volume 2, Issue 1, pp 101–112

Association schemes and quadratic transformations for orthogonal polynomials


  • Laura Chihara
    • Department of MathematicsSt. Olaf College
  • Dennis Stanton
    • School of MathematicsUniversity of Minnesota

DOI: 10.1007/BF01788084

Cite this article as:
Chihara, L. & Stanton, D. Graphs and Combinatorics (1986) 2: 101. doi:10.1007/BF01788084


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.

Copyright information

© Springer-Verlag 1986