This is an essentially self-contained monograph in an intriguing 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 double Hecke algebra technique. Visit http://arxiv.org/math.QA/0404307 to read Chapter 0 and selected topics from other chapters.Read more
- Was the first book on Double Affine Heck Algebras
- One of the main texts on Knizhnik-Zamolodchikov equations and their quantum counterparts, and also in the modern theory of spherical and hypergeometric functions
- See also http://arxiv.org/abs/math.QA/0404307
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'I think that this book will be of interest to both mathematicians and physicists who care about double Hecke algebra techniques.' Zentralblatt MATH
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- Date Published: March 2005
- format: Paperback
- isbn: 9780521609180
- length: 448 pages
- dimensions: 229 x 152 x 25 mm
- weight: 0.65kg
- availability: Available
Table of Contents
1. KZ and QMBP
2. One-dimensional DAHA
3. General theory.
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