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Macdonald-Koornwinder polynomials and affine Hecke algebras

Macdonald-Koornwinder polynomials and affine Hecke algebras
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Vanishing Integrals of Macdonald and Koornwinder polynomials

Transformation Groups, 2007
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,t-analogues of this fact were conjectured in [10]; the present paper proves most of those conjectures, as well as some new ...
Eric M. Rains, Monica Vazirani
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A new property of a class of Koornwinder Laguerre polynomials

Integral Transforms and Special Functions, 2014
A new property of a class of Koornwinder's Laguerre polynomials is established. In this context, new classes of stable polynomials and polynomial pairs with real negative and interlacing roots are introduced. As a result, the distribution of zeros of a class of Mittag-Leffler functions is proved and new multiplier sequences are introduced.
Marios Charalambides
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Koornwinder’s polynomials and representations of the conformal group

Journal of Mathematical Physics, 1979
The tensor product of two massive, spinless, positive-energy ray representations of the conformal group of spacetime SO0(4,2)/Z2 is reduced in a momentum basis. The basis vectors for the irreducible subspaces (the ’’Clebsch–Gordan coefficients’’) are found to be intimately connected with Koornwinder’s polynomials in two dimensions.
Maalee AlMheidat, Mohammad AlQudah
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Generalized Jacobi–Koornwinder’s-type Bernstein polynomials bases transformations

International Journal of Mathematics, 2016
This paper provides an explicit closed form of generalized Jacobi–Koornwinder’s polynomials of degree [Formula: see text] in terms of the Bernstein basis of fixed degree [Formula: see text] Moreover, explicit forms of generalized Jacobi–Koornwinder’s type and Bernstein polynomials bases transformations are considered.
AlQudah, Mohammad A., AlMheidat, Maalee N.   +1 more
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Generalized Gegenbauer Koornwinder’s type polynomials change of bases

AIP Conference Proceedings, 2017
In this paper we characterize the generalized Gegenbauer polynomials using Bernstein basis, and derive the matrix of transformation of the generalized Gegenbauer polynomial basis form into the Bernstein polynomial basis and vice versa.
Mohammad AlQudah, Maalee AlMheidat
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Lecture notes on Koornwinder polynomials

, 2004
Jasper V. Stokman
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Elliptic Analogues of the Macdonald and Koornwinder Polynomials

Proceedings of the International Congress of Mathematicians 2010 (ICM 2010), 2011
Perhaps the nicest multivariate orthogonal polynomials are the Macdonald and Koornwinder polynomials, respectively 2-parameter deformations of Schur functions and 6-parameter deformations of orthogonal and symplectic characters, satisfying a trio of nice properties known as the Macdonald “conjectures”.
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An algebraic approach to Macdonald–Koornwinder polynomials: Rodrigues-type formula and inner product identity

Journal of Mathematical Physics, 2001
We study Macdonald–Koornwinder polynomials in the context of double affine Hecke algebras. Nonsymmetric Macdonald–Koornwinder polynomials are constructed by use of raising operators provided by a representation theory of the double affine Hecke algebra associated with A2l(2)-type affine root system.
Nishino, Akinori, Komori, Yasushi
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Comparison of Sequence of Physical Processes (SPP) and Fourier Transform Coupled with Chebyshev Polynomials (FTC) methods to Interpret Large Amplitude Oscillatory Shear (LAOS) Response of Viscoelastic Doughs and Viscous Pectin Solution

Food Hydrocolloids, 2022
Merve Yildirim Erturk, Simon A Rogers, Jozef L Kokini   +2 more
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