Koornwinder polynomials and affine Hecke algebras
International Mathematics Research Notices, 2000 In this paper we derive the bi-orthogonality relations, diagonal term evaluations and evaluation formulas for the non-symmetric Koornwinder polynomials. For the derivation we use certain representations of the (double) affine Hecke algebra which were originally defined by Noumi and Sahi.
Jasper V. Stokman
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Rhombic staircase tableaux and Koornwinder polynomials
Mathematische Zeitschrift, 2023 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 +2 more
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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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Specializing Koornwinder polynomials to Macdonald polynomials of type B, C, D and BC [PDF]
Journal of Algebraic Combinatorics, 2022 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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Branching Rules for Koornwinder Polynomials with One Column Diagrams and Matrix Inversions [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2020 We present an explicit formula for the transition matrix $\mathcal{C}$ from the type $BC_n$ Koornwinder polynomials $P_{(1^r)}(x|a,b,c,d|q,t)$ with one column diagrams, to the type $BC_n$ monomial symmetric polynomials $m_{(1^{r})}(x)$. The entries of the matrix $\mathcal{C}$ enjoy a set of four terms recursion relations.
Ayumu Hoshino, Jun’ichi Shiraishi
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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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BC-type interpolation Macdonald polynomials and binomial formula for Koornwinder polynomials [PDF]
Transformation Groups, 1998 28 pages, AMS TeX; replaced with revised journal version, to appear in Transf ...
Andreĭ Okounkov
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Quasi-polynomial extensions of nonsymmetric Macdonald-Koornwinder polynomials [PDF]
43 pages; v2: minor ...
Jasper V. Stokman
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Minimal cubature rules and Koornwinder polynomials [PDF]
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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A Littlewood-Richardson rule for Koornwinder polynomials
, 2020 Koornwinder polynomials are $q$-orthogonal polynomials equipped with extra five parameters and the $B C_n$-type Weyl group symmetry, which were introduced by Koornwinder (1992) as multivariate analogue of Askey-Wilson polynomials. They are now understood as the Macdonald polynomials associated to the affine root system of type $(C^\vee_n,C_n)$ via the ...
Kohei Yamaguchi
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