Double Affine Hecke Algebras

English

Series: London Mathematical Society Lecture Note Ser.

Volume: Vol. 319

ISBN: 0511111657

EAN: 9780511111655

Category: Mathematics / Mathematical Analysis

Publisher: Cambridge University Press

Release Date: 03/24/2005

Synopsis: 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.

Excerpt: Unknown Property Excerpt

Double Affine Hecke Algebras

Illustrated: No

Format: eBook - PDF

Pages: 446