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 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.

ISBN 0521824729   Volumes 1 ISBN13 9780521824729 (What's this?)   Weight (grammes) 450 Publisher Cambridge University Press   Published in Cambridge Imprint Cambridge University Press   Series editor Bollobas, B., Fulton, W., Katok, A. Format Hardback   Series ISSN 157 Publication date 20 Mar 2003   Series title Cambridge Tracts in Mathematics Library of Congress QA174.2 .M28 2003   Height (mm) 228 DEWEY 512.942   Width (mm) 152 DEWEY edition DC21   Spine width (mm) 19 Pages 186   Academic level Professional / Scholarly

		Introduction
1		Affine root systems		1
1.1		Notation and terminology		1
1.2		Affine root systems		3
1.3		Classification of affine root systems		6
1.4		Duality		12
1.5		Labels		14
2		The extended affine Weyl group		17
2.1		Definition and basic properties		17
2.2		The length function on W		19
2.3		The Bruhat order on W		22
2.4		The elements u([lambda]'), v([lambda]')		23
2.5		The group [Omega]		27
2.6		Convexity		29
2.7		The partial order on L'		31
2.8		The functions r[subscript k'], r'[subscript k]		34
3		The braid group		37
3.1		Definition of the braid group		37
3.2		The elements Y[superscript [lambda]']		39
3.3		Another presentation of [actual symbol not reproducible]		42
3.4		The double braid group		45
3.5		Duality		47
3.6		The case R' = R		49
3.7		The case [actual symbol not reproducible]		52
4		The affine Hecke algebra		55
4.1		The Hecke algebra of W		55
4.2		Lusztig's relation		57
		More...

'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 fur Mathematik

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