Double Affine Hecke Algebras

Released on by Ivan Cherednik
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  • Double Affine Hecke Algebras Book Detail

  • Author : Ivan Cherednik
  • Release Date : 2005-03-24
  • Publisher : Cambridge University Press
  • Genre : Mathematics
  • Pages : 452
  • ISBN 13 : 9781139441254
  • File Size : 53,53 MB
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Double Affine Hecke Algebras by Ivan Cherednik PDF Summary

Book Description: 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.

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Studies in Lie Theory

Studies in Lie Theory

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Contains new results on different aspects of Lie theory, including Lie superalgebras, quantum groups, crystal bases, representations of reductive groups in fini