Affine Hecke Algebras and Orthogonal Polynomials

Cambridge Tracts in Mathematics

I.G. MacDonald

446 pages, parution le 17/03/2003

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Résumé

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 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 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.

Contents

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

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	I.G. MacDonald
Parution	17/03/2003
Nb. de pages	446
Format	15,5 x 23,5
Couverture	Relié
Poids	175g
Intérieur	Noir et Blanc
EAN13	9780521824729
ISBN13	978-0-521-82472-9