Results 21 to 30 of about 2,040 (118)

Representations for the parameter derivatives of some Koornwinder polynomials [PDF]

, 2015
In 1975, Koornwinder gave a method to construct orthogonal polynomials in two variables using the classical Jacobi polynomials. In [5], the authors introduced some new examples of Koornwinder polynomials obtained from the Koornwinder construction (see also [10]).
Rabıa Aktaş
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Specializations of nonsymmetric Macdonald-Koornwinder polynomials [PDF]

Journal of Algebraic Combinatorics, 2013
This work records the details of the Ram-Yip formula for nonsymmetric Macdonald-Koornwinder polynomials for the double affine Hecke algebras of not-necessarily-reduced affine root systems. It is shown that the t=0 equal-parameter specialization of nonsymmetric Macdonald polynomials admits an explicit combinatorial formula in terms of quantum alcove ...
Daniel L. Orr, Mark Shimozono
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Specializing Koornwinder polynomials to Macdonald polynomials of type $B,C,D$ and $B C$ [PDF]

Journal of Algebraic Combinatorics, 2021
We study the specializations of parameters in Koornwinder polynomials to obtain Macdonald polynomials associated to the subsystems of the affine root system of type $(C_n^\vee,C_n)$ in the sense of Macdonald (2003), and summarize them in what we call the specialization table. As a verification of our argument, we check the specializations to type $B,C$
Kohei Yamaguchi, Shintarou Yanagida
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Sparse Spectral-Galerkin Method on An Arbitrary Tetrahedron Using Generalized Koornwinder Polynomials [PDF]

Journal of Scientific Computing, 2021
29 pages, 24 ...
Lueling Jia, Huiyuan Li, Zhimin Zhang
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Shifted Macdonald polynomials with 3 parameters and binomial formula for Koornwinder polynomials [PDF]

Transformation Groups, 1996
28 pages, AMS TeX; replaced with revised journal version, to appear in Transf ...
Andreĭ Okounkov
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Quantum spherical functions of type $χ$ as Macdonald-Koornwinder polynomials [PDF]

31 ...
Stein Meereboer
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c -Functions and Koornwinder Polynomials [PDF]

The Quarterly Journal of Mathematics
ABSTRACT This paper develops the theory of Macdonald–Koornwinder polynomials in parallel analogy with the work done by us in 2024 for the $GL_n$ case [c-functions and Macdonald polynomials, J. Algebra 655 (2024), 163–222]. In the context of the type $(C^\vee _n, C_n)$ affine root system, the Macdonald polynomials of other root systems of
Laura Colmenarejo, Arun Ram
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Minimal cubature rules and Koornwinder polynomials [PDF]

Indagationes Mathematicae
In his classical paper [5], Koornwinder studied a family of orthogonal polynomials of two variables, derived from symmetric polynomials. This family possesses a rare property that orthogonal polynomials of degree $n$ have $n(n+1)/2$ real common zeros, which leads to important examples in the theory of minimal cubature rules.
Yuan Xu
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vector valued spherical functions and macdonald–koornwinder polynomials [PDF]

Compositio Mathematica, 2005
We interpret the five parameter family of Macdonald-Koornwinder polynomials as vector valued spherical functions on quantum Grassmannians.
Alexei Oblomkov, Jasper V. Stokman
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Some transformation formulas associated with Askey-Wilson polynomials and Lassalle's formulas for Macdonald-Koornwinder polynomials [PDF]

Moscow Mathematical Journal, 2014
We present a fourfold series expansion representing the Askey-Wilson polynomials. To obtain the result, a sequential use is made of several summation and transformation formulas for the basic hypergeometric series, including the Verma's q-extension of the Field and Wimp expansion, Andrews' terminating q-analogue of Watson's 3F2 sum, Singh's quadratic ...
Ayumu Hoshino, Masatoshi Noumi, Junji Shiraishi   +2 more
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