TY - BOOK ID - 18196809 TI - Affine Hecke algebras and orthogonal polynomials PY - 2003 SN - 0521824729 0511062354 9780511062353 9780521824729 0511070810 9780511070815 9780511542824 0511542828 1107137454 1280436727 9786610436729 0511179170 1139149059 0511056028 0511306229 PB - Cambridge, UK New York Cambridge University Press DB - UniCat KW - Hecke algebras. KW - Orthogonal polynomials. KW - 512.55 KW - 517.518 KW - Hecke algebras KW - Orthogonal polynomials KW - Fourier analysis KW - Functions, Orthogonal KW - Polynomials KW - Algebras, Hecke KW - Group algebras KW - 517.518 Metric theory of functions KW - Metric theory of functions KW - 512.55 Rings and modules KW - Rings and modules UR - https://www.unicat.be/uniCat?func=search&query=sysid:18196809 AB - 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. ER -