Double Affine Hecke Algebras (London Mathematical Society Lecture Note Series, Series Number 319) by Ivan Cherednik (PDF)

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.

User’s Reviews

Editorial Reviews: Review ‘I think that this book will be of interest to both mathematicians and physicists who care about double Hecke algebra techniques.’ Zentralblatt MATH Book Description This is an essentially self-contained monograph centered on the new double Hecke algebra technique.

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