Affine Hecke Algebras and Orthogonal Polynomials

First account of a theory, created by Macdonald, of a class of orthogonal polynomial, which is related to mathematical physics.

I. G. Macdonald (Author)

9780521824729, Cambridge University Press

Hardback, published 20 March 2003

186 pages
23.1 x 15.5 x 1.5 cm, 0.41 kg

'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 systems in two or more parameters.' Zentralblatt für Mathematik

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 Askey–Wilson 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.

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.

Subject Areas: Applied mathematics [PBW], Algebra [PBF], Mathematical foundations [PBC]