A satisfactory and coherent theory of orthogonal polynomials in several variables, attached to root systems, and depending on two or more parameters, has developed in recent years. This comprehensive account of the subject provides a unified foundation for the theory to which I.G. Macdonald has been a principal contributor. The first four chapters lead up to Chapter 5 which contains all the main results.

One of the most classical areas of algebra, the theory of symmetric functions and orthogonal polynomials, has long been known to be connected to combinatorics, representation theory and other branches of mathematics. This volume explains developments regarding these connections. It is based on lectures presented by the author at Rutgers University. Specifically, he gives recent results on orthogonal polynomials associated with affine Hecke algebras, surveying the proofs of certain famous combinatorial conjectures.

This reissued classic text is the acclaimed second edition of Professor Ian Macdonald's groundbreaking monograph on symmetric functions and Hall polynomials.
The first edition was published in 1979, before being significantly expanded into the present edition in 1995. This text is widely regarded as the best source of information on Hall polynomials and what have come to be known as Macdonald polynomials, central to a number of key developments in mathematics and mathematical physics in the 21st century
Macdonald polynomials gave rise to the subject of double affine Hecke algebras (or...