Piotr Pragacz


Introduction to Macdonald functions


Macdonald polynomials $P_{\lambda}(x; t,q)$ are a family of orthogonal polynomials in several variables, introduced by Ian Macdonald in 1987. They generalize many other families of orthogonal polynomials, such as Jack polynomials, Hall–Littlewood polynomials and Askey–Wilson polynomials. They have deep relationships with affine Hecke algebras and Hilbert schemes, which were used to prove several conjectures made by Macdonald about them.