Macdonald-Koornwinder polynomials
Jasper V. Stokman
TL;DR
This paper provides a comprehensive overview of Macdonald-Koornwinder polynomials, covering their fundamental properties and their relation to double affine Hecke algebras, unifying known cases within a broad theoretical framework.
Contribution
It develops a unified theory of Macdonald-Koornwinder polynomials that encompasses all known cases, including properties like norm formulas, duality, and evaluation formulas.
Findings
Unified framework for Macdonald-Koornwinder polynomials
Derivation of quadratic norm formulas
Establishment of duality and evaluation formulas
Abstract
An overview of the basic results on Macdonald(-Koornwinder) polynomials and double affine Hecke algebras is given. We develop the theory in such a way that it naturally encompasses all known cases. Among the basic properties of the Macdonald polynomials we treat are the quadratic norm formulas, duality and the evaluation formulas. This text is a provisional version of a chapter on Macdonald polynomials for volume 5 of the Askey-Bateman project, entitled "Multivariable special functions".
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Taxonomy
TopicsAdvanced Mathematical Identities · Molecular spectroscopy and chirality · Advanced Combinatorial Mathematics