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The Macdonald polynomials are polynomials in n variables x=(x 1,...,x n), where n is the rank of the affine root system. They generalize many other families of orthogonal polynomials, such as Jack polynomials and Hall–Littlewood polynomials and Askey–Wilson polynomials , which in turn include most of the named 1-variable orthogonal ...
Waleed Al-Salam (1926–1996): Al-Salam polynomial - Al Salam–Carlitz polynomial - Al Salam–Chihara polynomial; C. T. Anger: Anger–Weber function; Kazuhiko Aomoto: Aomoto–Gel'fand hypergeometric function - Aomoto integral; Paul Émile Appell (1855–1930): Appell hypergeometric series, Appell polynomial, Generalized Appell polynomials
Using this he was able to give a proof of Macdonald's constant term conjecture for Macdonald polynomials (building on work of Eric Opdam). Another main inspiration for Cherednik to consider the double affine Hecke algebra was the quantum KZ equations .
The affine root system of type G 2.. In mathematics, an affine root system is a root system of affine-linear functions on a Euclidean space.They are used in the classification of affine Lie algebras and superalgebras, and semisimple p-adic algebraic groups, and correspond to families of Macdonald polynomials.
In mathematics, Macdonald-Koornwinder polynomials (also called Koornwinder polynomials) are a family of orthogonal polynomials in several variables, introduced by Koornwinder [1] and I. G. Macdonald, [2] that generalize the Askey–Wilson polynomials. They are the Macdonald polynomials attached to the non-reduced affine root system of type (C ∨
The Macdonald polynomials are a two-parameter family of orthogonal polynomials indexed by a positive weight λ of a root system, introduced by Ian G. Macdonald (1987). They generalize several other families of orthogonal polynomials, such as Jack polynomials and Hall–Littlewood polynomials.
A. A. Kirillov Lectures on affine Hecke algebras and Macdonald's conjectures Bull. Amer. Math. Soc. 34 (1997), 251–292. Macdonald, I. G. Affine Hecke algebras and orthogonal polynomials. Cambridge Tracts in Mathematics, 157. Cambridge University Press, Cambridge, 2003. x+175 pp. ISBN 0-521-82472-9 MR 1976581
In mathematics, the Hall–Littlewood polynomials are symmetric functions depending on a parameter t and a partition λ. They are Schur functions when t is 0 and monomial symmetric functions when t is 1 and are special cases of Macdonald polynomials.