Macdonald polynomials
In mathematics, Macdonald polynomials Pλ(x; t,q) are a family of orthogonal symmetric polynomials in several variables, introduced by Macdonald in 1987. He later introduced a non-symmetric generalization in 1995. Macdonald originally associated his polynomials with weights λ of finite root systems and used just one variable t, but later realized that it is more natural to associate them with affine root systems rather than finite root systems, in which case the variable t can be replaced by several different variables t=(t1,...,tk), one for each of the k orbits of roots in the affine root system. The Macdonald polynomials are polynomials in n variables x=(x1,...,xn), where n is the rank of the affine root system. They generalize many other families of orthogonal polynomials, such as Jack p
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Affine Hecke algebraAffine root systemAskey–Wilson polynomialsDouble affine Hecke algebraDyson conjectureHall–Littlewood polynomialsHeckman–Opdam polynomialsHilbert schemeIan G. MacdonaldIvan CherednikIwahori–Hecke algebraJack functionKoornwinder polynomialsKostka polynomialLLT polynomialLauren Williams (mathematician)List of polynomial topicsList of special functions and eponymsList of unsolved problems in mathematicsMAcdonald constant term conjectureMacdonald's constant-term conjectureMacdonald's constant term conjectureMacdonald's positivity conjectureMacdonald (disambiguation)Macdonald conjectureMacdonald constant term conjectureMacdonald polynomialMacdonald positivity conjectureMark HaimanN! conjectureN! theoremOrthogonal polynomialsRogers polynomialsSchur polynomialSylvie Corteel
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Macdonald polynomials
In mathematics, Macdonald polynomials Pλ(x; t,q) are a family of orthogonal symmetric polynomials in several variables, introduced by Macdonald in 1987. He later introduced a non-symmetric generalization in 1995. Macdonald originally associated his polynomials with weights λ of finite root systems and used just one variable t, but later realized that it is more natural to associate them with affine root systems rather than finite root systems, in which case the variable t can be replaced by several different variables t=(t1,...,tk), one for each of the k orbits of roots in the affine root system. The Macdonald polynomials are polynomials in n variables x=(x1,...,xn), where n is the rank of the affine root system. They generalize many other families of orthogonal polynomials, such as Jack p
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In mathematics, Macdonald poly ...... made by Macdonald about them.
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In mathematics, Macdonald poly ...... al polynomials, such as Jack p
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Macdonald polynomials
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