Double Affine Hecke Algebras

Ivan Cherednik - Collection London Mathematical Society Student Texts

440 pages, parution le 01/04/2005

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Résumé

This is a unique, essentially self-contained, monograph in a new field of fundamental importance for Representation Theory, Harmonic Analysis, Mathematical Physics, and Combinatorics. It is a major source of general information about the double affine Hecke algebra, also called Cherednik's algebra, and its impressive applications. Chapter 1 is devoted to the Knizhnik-Zamolodchikov equations attached to root systems and their relations to affine Hecke algebras, Kac-Moody algebras, and Fourier analysis. Chapter 2 contains a systematic exposition of the representation theory of the one-dimensional DAHA. It is the simplest case but far from trivial with deep connections in the theory of special functions. Chapter 3 is about DAHA in full generality, including applications to Macdonald polynomials, Fourier transforms, Gauss-Selberg integrals, Verlinde algebras, and Gaussian sums. This book is designed for mathematicians and physicists, experts and students, for those who want to master the new double Hecke algebra technique. Visit http://arxiv.org/math.QA/0404307 to read Chapter 0 and selected topics from other chapters.

L'auteur - Ivan Cherednik

Ivan Cherednik: University of North Carolina, Chapel Hill

Sommaire

Introduction
KZ and QMBP
One-dimensional DAHA
General theory

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Ivan Cherednik
Collection	London Mathematical Society Student Texts
Parution	01/04/2005
Nb. de pages	440
Format	15,5 x 22,5
Couverture	Broché
Poids	620g
Intérieur	Noir et Blanc
EAN13	9780521609180
ISBN13	978-0-521-60918-0