Results 71 to 80 of about 2,393 (108)
Nonsymmetric Askey–Wilson polynomials and Q-polynomial distance-regular graphs
Journal of Combinatorial Theory, Series A, 2017 In his famous theorem (1982), Douglas Leonard characterized the $q$-Racah polynomials and their relatives in the Askey scheme from the duality property of $Q$-polynomial distance-regular graphs. In this paper we consider a nonsymmetric (or Laurent) version of the $q$-Racah polynomials in the above situation.
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On First type characterizations of Askey-Wilson polynomials
, 2023 In this chapter we characterize Askey-Wilson polynomials including specific and limiting cases of them by some structure relations of the first type.
Mbouna, D., Suzuki, A.
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8 Lectures on quantum groups and q-special functions [PDF]
, 1996 Lecture notes for an eight hour course on quantum groups and $q$-special functions at the fourth Summer School in Differential Equations and Related Areas, Universidad Nacional de Colombia and Universidad de los Andes, Bogot\'a, Colombia, July 22 ...
Koelink, Erik
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Askey-Wilson polynomials: an affine Hecke algebraic approach
, 2000 We study Askey-Wilson type polynomials using representation theory of the double affine Hecke algebra. In particular, we prove bi-orthogonality relations for non-symmetric and anti-symmetric Askey-Wilson polynomials with respect to a complex measure.
Noumi, M., Stokman, J.V.
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A "missing" family of classical orthogonal polynomials
, 2011 We study a family of "classical" orthogonal polynomials which satisfy (apart from a 3-term recurrence relation) an eigenvalue problem with a differential operator of Dunkl-type.
Alexei Zhedanov +15 more
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Convolutions for orthogonal polynomials from Lie and quantum algebra representations
, 1996 The interpretation of the Meixner-Pollaczek, Meixner and Laguerre polynomials as overlap coefficients in the positive discrete series representations of the Lie algebra su(1,1) and the Clebsch-Gordan decomposition leads to generalisations of the ...
Koelink, H. T., Van der Jeugt, J.
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A Quantum Algebra Approach to Multivariate Askey–Wilson Polynomials [PDF]
International Mathematics Research Notices, 2019 AbstractWe study matrix elements of a change of basis between two different bases of representations of the quantum algebra ${\mathcal{U}}_q(\mathfrak{s}\mathfrak{u}(1,1))$. The two bases, which are multivariate versions of Al-Salam–Chihara polynomials, are eigenfunctions of iterated coproducts of twisted primitive elements.
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Harmonic analysis on the SU(2) dynamical quantum group
, 2001 Dynamical quantum groups were recently introduced by Etingof and Varchenko as an algebraic framework for studying the dynamical Yang-Baxter equation, which is precisely the Yang-Baxter equation satisfied by 6j-symbols.
Koelink, Erik, Rosengren, Hjalmar
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Terminating Basic Hypergeometric Representations and Transformations for the Askey-Wilson Polynomials. [PDF]
Symmetry (Basel), 2020 Cohl HS, Costas-Santos RS, Ge L.
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FCAA Special 2020 Conferences' Issue (FCAA-Volume 23-6-2020). [PDF]
Fract Calc Appl Anal, 2020 Kiryakova V.
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