q-Selberg Integrals and Koornwinder Polynomials [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2022 We prove a generalization of the q-Selberg integral evaluation formula. The integrand is that of q-Selberg integral multiplied by a factor of the same form with respect to part of the variables.
Jyoichi Kaneko
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Branching formula for Macdonald–Koornwinder polynomials [PDF]
, 2015 J. F. van Diejen, E. Emsiz
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Rhombic staircase tableaux and Koornwinder polynomials [PDF]
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 $\tilde{C}$.
Sylvie Corteel +2 more
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Koornwinder polynomials and the
Journal of Approximation Theory, 2014 Jasper V. Stokman, Bart Vlaar
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Quasi-Polynomial Extensions of Nonsymmetric Macdonald-Koornwinder Polynomials [PDF]
Symmetry, Integrability and Geometry: Methods and ApplicationsIn a recent joint paper with S. Sahi and V. Venkateswaran (2025), families of actions of the double affine Hecke algebra on spaces of quasi-polynomials were introduced.
Jasper V. Stokman
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Matrix product construction for Koornwinder polynomials and fluctuations of the current in the open ASEP [PDF]
, 2017 Starting from the deformed current-counting transition matrix for the open boundary ASEP, we prove that with a further deformation, the symmetric Koornwinder polynomials for partitions with equal row lengths appear as the normalisation of the twice ...
Caley Finn, Matthieu Vanicat
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QBD Processes Associated with Jacobi–Koornwinder Bivariate Polynomials and Urn Models [PDF]
Mediterranean Journal of Mathematics, 2023 We study a family of quasi-birth-and-death (QBD) processes associated with the so-called first family of Jacobi–Koornwinder bivariate polynomials. These polynomials are orthogonal on a bounded region typically known as the swallow tail.
Lidia Fernández +1 more
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Representations for parameter derivatives of some Koornwinder polynomials in two variables
, 2016 Rabıa Aktaş
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Branching Rules for Koornwinder Polynomials with One Column Diagrams and Matrix Inversions [PDF]
, 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 $m_{(1^{r})}(x)$.
Ayumu Hoshino, Jun’ichi Shiraishi
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Koornwinder polynomials and the stationary multi-species asymmetric exclusion process with open boundaries [PDF]
, 2016 We prove that the normalisation of the stationary state of the multi-species asymmetric simple exclusion process (mASEP) is a specialisation of a Koornwinder polynomial.
Cantini, Luigi +3 more
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