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Double Affine Hecke Algebras

$110.00 (C)

Part of London Mathematical Society Lecture Note Series

  • Date Published: April 2005
  • availability: Available
  • format: Paperback
  • isbn: 9780521609180

$ 110.00 (C)
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  • 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.

    • 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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    Reviews & endorsements

    '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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    Product details

    • Date Published: April 2005
    • format: Paperback
    • isbn: 9780521609180
    • length: 448 pages
    • dimensions: 229 x 152 x 25 mm
    • weight: 0.65kg
    • availability: Available
  • Table of Contents

    0. Introduction
    1. KZ and QMBP
    2. One-dimensional DAHA
    3. General theory.

  • Author

    Ivan Cherednik, University of North Carolina, Chapel Hill

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