num_pages: 448
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.
language: English
title: Double Affine Hecke Algebras
publisher: Cambridge University Press