ENGLISH

Double Affine Hecke Algebras

By Ivan Cherednik

Book information

Publisher
Cambridge University Press
Year
2005
ISBN
9780511113185, 9780511546501, 9780521609180, 0521609186
Language
english
Format
PDF
Filesize
3 MB (3293361 bytes)
Series
London Mathematical Society Lecture Note Series
Pages
447\447
Time added
2011-06-04 13:46:07

Description

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, all those who want to master the new double Hecke algebra technique.

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