Affine Hecke Algebras and Orthogonal Polynomials

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. These polynomials include as special cases: symmetric functions; zonal spherical functions on real and p-adic reductive Lie groups; the Jacobi polynomials of Heckman and Opdam; and the AskeyâWilson polynomials which themselves include as special or limiting cases all the classical families of orthogonal polynomials in one variable. This book first published in 2003 is a 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 an essentially self-contained treatment accessible to graduate students familiar with root systems and Weyl groups. 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. Language: English