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High Quality Content by WIKIPEDIA articles! In mathematics, Macdonald polynomials P are a two-parameter family of orthogonal polynomials indexed by a positive weight of a root system, introduced by Ian G. Macdonald (1987). They generalize several other families of orthogonal polynomials, such as Jack polynomials and Hall Littlewood polynomials. They have deep relationships with affine Hecke algebras and Hilbert schemes, which were used to prove several conjectures made by Macdonald about them.