Results 11 to 20 of about 2,254 (120)
Self-dual Koornwinder-Macdonald polynomials [PDF]
Inventiones Mathematicae, 1995 We prove certain duality properties and present recurrence relations for a four-parameter family of self-dual Koornwinder-Macdonald polynomials. The recurrence relations are used to verify Macdonald's normalization conjectures for these polynomials ...
van Diejen, Jan F.
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Symmetric and nonsymmetric Koornwinder polynomials in the q → 0 limit [PDF]
Journal of Algebraic Combinatorics, 2016 Koornwinder polynomials are a 6-parameter BC[subscript n]-symmetric family of Laurent polynomials indexed by partitions, from which Macdonald polynomials can be recovered in suitable limits of the parameters. As in the Macdonald polynomial case, standard
Venkateswaran, Vidya
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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. The proof relies on the quadratic norm formula of Koornwinder polynomials.
Jyoichi Kaneko
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Branching formula for Macdonald–Koornwinder polynomials [PDF]
Journal of Algebra, 2015 8 pages ...
J. F. van Diejen, E. Emsiz
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Macdonald–Koornwinder Polynomials [PDF]
, 2020 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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Bivariate Koornwinder–Sobolev Orthogonal Polynomials [PDF]
Mediterranean Journal of Mathematics, 2021 AbstractThe so-called Koornwinder bivariate orthogonal polynomials are generated by means of a non-trivial procedure involving two families of univariate orthogonal polynomials and a function $$\rho (t)$$ ρ ( t ) such ...
Misael E. Marriaga +2 more
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Nonsymmetric Koornwinder Polynomials and Duality [PDF]
The Annals of Mathematics, 1999 16 pages, published ...
Siddhartha Sahi
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An asymptotic formula for the Koornwinder polynomials
Journal of Computational and Applied Mathematics, 2004 AbstractA formula for the large-degree asymptotics of Koornwinder's multivariate Askey–Wilson polynomials is presented. In the special case of a single variable, this asymptotic formula agrees with the known leading asymptotics of the Askey–Wilson polynomials determined by Ismail and Wilson.
J. F. van Diejen
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QBD Processes Associated with Jacobi–Koornwinder Bivariate Polynomials and Urn Models [PDF]
Mediterranean Journal of Mathematics, 2023 AbstractWe 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. We will explicitly compute the coefficients of the three-term recurrence relations generated by these QBD ...
Lidia Fernández +1 more
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$c$-functions and Koornwinder polynomials [PDF]
This paper develops the theory of Macdonald-Koornwinder polynomials in parallel analogy with the work done for the $GL_n$ case in [CR22]. In the context of the type $CC_n$ affine root system the Macdonald polynomials of other root systems of classical type are specializations of the Koornwinder polynomials.
Laura Colmenarejo, Arun Ram
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