Affine Hecke Algebras and Orthogonal Polynomials [Hardcover]

First account of a theory, created by Macdonald, of a class of orthogonal polynomial, which is related to mathematical physics.In recent years there has developed a satisfactory and coherent theory of orthogonal polynomials in several variables, attached to root systems, and depending on two or more parameters. This Tract, which is the first comprehensive and organised account of the subject, aims to provide a unified foundation for this theory, to which the author has been a principal contributor. It is essentially self-contained: the first four chapters are preparatory to Chapter V, which is the heart of the book and contains all the main results in full generality.In recent years there has developed a satisfactory and coherent theory of orthogonal polynomials in several variables, attached to root systems, and depending on two or more parameters. This Tract, which is the first comprehensive and organised account of the subject, aims to provide a unified foundation for this theory, to which the author has been a principal contributor. It is essentially self-contained: the first four chapters are preparatory to Chapter V, which is the heart of the book and contains all the main results in full generality.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.Introduction; 1. Affine root systems; 2. The extended affine Weyl group; 3. The braid group; 4. The affine Hecke algebra; 5. Orthogonal polynomials; 6. The rank 1 case; Bibliography; Index.'This is a beautiful book, treating in a concise and clear way the recent developments concerning the connection between orthogonal polynomials in several variables and root systlC*