Results 11 to 20 of about 157 (102)

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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Macdonald-Koornwinder polynomials [PDF]

, 2011
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.
Jasper V. Stokman
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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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Asymmetric Simple Exclusion Process with Open Boundaries and Koornwinder Polynomials [PDF]

Annales Henri Poincaré, 2017
35 ...
Luigi Cantini
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Quadratic transformations of Macdonald and Koornwinder polynomials [PDF]

, 2006
When one expands a Schur function in terms of the irreducible characters of the symplectic (or orthogonal) group, the coefficient of the trivial character is 0 unless the indexing partition has an appropriate form. A number of q-analogues of this fact were conjectured in math.QA/0112035; the present paper proves most of those conjectures, as well as ...
Eric M. Rains, Monica Vazirani
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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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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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Rhombic staircase tableaux and Koornwinder polynomials

Mathematische Zeitschrift
In this article we give a combinatorial formula for a certain class of Koornwinder polynomials, also known as Macdonald polynomials of type $\tilde{C}$. In particular, we give a combinatorial formula for the Koornwinder polynomials $K_λ = K_λ(z_1,\dots,z_N; a,b,c,d; q,t)$, where $λ= (1,\dots,1,0,\dots,0)$.
Sylvie Corteel, Olya Mandelshtam, Lauren Williams   +2 more
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An asymptotic formula for the Koornwinder polynomials

Journal of Computational and Applied Mathematics, 2004
This paper incorporates the derivation of a leading asymptotic formula for Koornwinder multivariate Askey-Wilson polynomials whose degree tends to infinity. For the single variable case the asymptotic formula derived here is shown to be in agreement with the known corresponding result for Askey-Wilson polynomials.
J. F. van Diejen
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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]).
Rabi̇a Aktaş
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