Affine Hecke Algebras and Orthogonal Polynomials (Cambridge Tracts in Mathematics)
Publisher: Cambridge University Press
Published: April 14, 2003
Language: eng
Format: Hardcover
Number of pages: 186
ISBN-13: 9780521824729
Subjects: Algebra; Applied mathematics; Mathematical foundations; Mathematics; Algebras; Polynomials; Science/Mathematics; Orthogonal polynomials; Algebra - Linear; General; Mathematics / Algebra / General; Finite Mathematics; Group Theory; Hecke algebras
First sentence: Let E be an affine space over a field K: that is to say, E is a set on which a K-vector space V acts faithfully and transitively.
Description: Publisher Description (unedited publisher data) 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 first 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.