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9 - Macdonald–Koornwinder Polynomials

Published online by Cambridge University Press:  30 September 2020

By
J. V. Stokman
Edited by
Tom H. Koornwinder  and
Jasper V. Stokman
Tom H. Koornwinder
Affiliation:
Universiteit van Amsterdam
Jasper V. Stokman
Affiliation:
Universiteit van Amsterdam
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Summary

This chapter gives an overview of the theory of nonsymmetric and symmetric Macdonald-Koornwinder polynomials. The setup of the theory is new, allowing for a uniform treatment of all known cases, including a new rank two case. Among the basic properties of the Macdonald-Koornwinder polynomials discussed in the chapter are the (bi)orthogonality relations, the quadratic norm formulas, duality, and evaluation formulas. The chapter also gives an introduction to the associated theory of double affine Hecke algebras.

Keywords

Macdonald-Koornwinder polynomialsmultivariable basic hypergeometric orthogonal polynomials associated with root systemsdouble affine Hecke algebras
Type
Chapter
Information
Encyclopedia of Special Functions: The Askey-Bateman Project , pp. 258 - 313
Publisher: Cambridge University Press
Print publication year: 2020

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