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Affine Hecke Algebras and Orthogonal Polynomials

Affine Hecke Algebras and Orthogonal Polynomials

£91.99

Part of Cambridge Tracts in Mathematics

  • Date Published: March 2003
  • availability: Available
  • format: Hardback
  • isbn: 9780521824729

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  • In recent years there has developed a satisfactory and coherent theory of orthogonal polynomials in several variables, attached to root systems, and depending on two or more parameters. These polynomials include as special cases: symmetric functions; zonal spherical functions on real and p-adic reductive Lie groups; the Jacobi polynomials of Heckman and Opdam; and the Askey–Wilson polynomials, which themselves include as special or limiting cases all the classical families of orthogonal polynomials in one variable. This book, first published in 2003, is a comprehensive and organised account of the subject aims to provide a unified foundation for this theory, to which the author has been a principal contributor. It is an essentially self-contained treatment, accessible to graduate students familiar with root systems and Weyl groups. The first four chapters are preparatory to Chapter V, which is the heart of the book and contains all the main results in full generality.

    • First comprehensive and organised account of the subject; much of the material has never appeared in book form before
    • Author is one of the leading authorities worldwide on this topic, and indeed is its creator
    • Despite the modernity of the subject, the account is self-contained and accessible for graduate students in algebra
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    Reviews & endorsements

    'This is a beautiful book, treating in a concise and clear way the recent developments concerning the connection between orthogonal polynomials in several variables and root systems in two or more parameters.' Zentralblatt für Mathematik

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    Product details

    • Date Published: March 2003
    • format: Hardback
    • isbn: 9780521824729
    • length: 186 pages
    • dimensions: 231 x 155 x 15 mm
    • weight: 0.41kg
    • availability: Available
  • Table of Contents

    Introduction
    1. Affine root systems
    2. The extended affine Weyl group
    3. The braid group
    4. The affine Hecke algebra
    5. Orthogonal polynomials
    6. The rank 1 case
    Bibliography
    Index.

  • Author

    I. G. Macdonald, Queen Mary University of London

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