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Double Affine Hecke Algebras by Ivan Cherednik

Double Affine Hecke Algebras

by Ivan Cherednik
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Book cover type: Paperback
  • ISBN13: 9780521609180
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Cambridge University Press
  • Publisher Imprint: Cambridge University Press
  • Publication Date:
  • Pages: 448
  • Original Price: USD 116.0
  • Language: English
  • Edition: N/A
  • Item Weight: 635 grams
  • BISAC Subject(s): Algebra / General

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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