Double Affine Hecke Algebras (London Mathematical Society Lecture Note Series) by Ivan Cherednik
English | 2005-04-11 | ISBN: 0521609186 | 447 pages | PDF | 3 mb
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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