Results 11 to 20 of about 2,040 (118)
Branching formula for Macdonald–Koornwinder polynomials [PDF]
Journal of Algebra, 2015 8 pages ...
J. F. van Diejen, E. Emsiz
openalex +4 more sources
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
openalex +4 more sources
A Littlewood-Richardson rule for Koornwinder polynomials [PDF]
Journal of Algebraic Combinatorics, 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
openalex +4 more sources
Self-dual Koornwinder-Macdonald polynomials [PDF]
Inventiones Mathematicae, 1996 21 pages, AMSLaTeX 1.1 with ...
J. F. van Diejen
openalex +5 more sources
Koornwinder polynomials and affine Hecke algebras [PDF]
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
openalex +4 more sources
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
openalex +3 more sources
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
+7 more sources
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
openalex +6 more sources
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
openalex +5 more sources
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. These so-called quasi-polynomial representations led to the introduction of quasi-polynomial extensions of the nonsymmetric Macdonald polynomials, which reduce to metaplectic Iwahori ...
Jasper V. Stokman
+6 more sources