Multivariable Wilson polynomials and degenerate Hecke algebras [PDF]
Selecta Mathematica, 2007 We study a rational version of the double affine Hecke algebra associated to the nonreduced affine root system of type $(C^\vee_n,C_n)$. A certain representation in terms of difference-reflection operators naturally leads to the definition of nonsymmetric versions of the multivariable Wilson polynomials.
Wolter Groenevelt
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Askey-Wilson Polynomials and Branching Laws
, 2022 Connection coefficient formulas for special functions describe change of basis matrices under a parameter change, for bases formed by the special functions. Such formulas are related to branching questions in representation theory. The Askey-Wilson polynomials are one of the most general 1-variable special functions.
Allen Back +3 more
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Two Families of Associated Wilson Polynomials [PDF]
Canadian Journal of Mathematics, 1990 AbstractTwo families of associated Wilson polynomials are introduced. Both families are birth and death process polynomials, satisfying the same recurrence relation but having different initial conditions. Contiguous relations for generalized hypergeometric functions of the type 7F6 are derived and used to find explicit representations for the ...
Mourad E. H. Ismail +3 more
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Generalized Bochner theorem: Characterization of the Askey–Wilson polynomials
Journal of Computational and Applied Mathematics, 2006 Assume that there is a set of monic polynomials $P_n(z)$ satisfying the second-order difference equation $$ A(s) P_n(z(s+1)) + B(s) P_n(z(s)) + C(s) P_n(z(s-1)) = _n P_n(z(s)), n=0,1,2,..., N$$ where $z(s), A(s), B(s), C(s)$ are some functions of the discrete argument $s$ and $N$ may be either finite or infinite. The irreducibility condition $A(s-1)C(
Luc Vinet, Alexei Zhedanov
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Nonsymmetric Askey-Wilson polynomials and Q-polynomial distance-regular graphs [PDF]
Journal of Combinatorial Theory, 2015 Jae-Ho Lee
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Correction To: Jacobi Ensemble, Hurwitz Numbers and Wilson Polynomials
Letters in Mathematical Physics, 2023 (1.1) Here CN := ∫ HN (I ) exp tr V (X)dX and V = V (x) is a smooth function of x ∈ I ◦ (the interior of I ) so that V (X) is defined for all X ∈ HN (I ) by the spectral theorem. We assume that V satisfies the following decay assumptions: there exists ε >
Massimo Gisonni, T. Grava, Giulio Ruzza
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Degenerate Sklyanin algebras, Askey–Wilson polynomials and Heun operators [PDF]
Journal of Physics A: Mathematical and Theoretical, 2020 The q-difference equation, the shift and the contiguity relations of the Askey–Wilson polynomials are cast in the framework of the three and four-dimensional degenerate Sklyanin algebras ska3 and ska4 .
J. Gaboriaud +3 more
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Connection and linearization coefficients of the Askey-Wilson polynomials
Journal of symbolic computation, 2013 M. Foupouagnigni +2 more
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A Quantum Algebra Approach to Multivariate Askey–Wilson Polynomials [PDF]
International mathematics research notices, 2018 We study matrix elements of a change of basis between two different bases of representations of the quantum algebra ${\mathcal{U}}_q(\mathfrak{s}\mathfrak{u}(1,1))$.
W. Groenevelt
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Infinitely many shape invariant discrete quantum mechanical systems and new exceptional orthogonal polynomials related to the Wilson and Askey-Wilson polynomials [PDF]
, 2009 Two sets of infinitely many exceptional orthogonal polynomials related to the Wilson and Askey-Wilson polynomials are presented. They are derived as the eigenfunctions of shape invariant and thus exactly solvable quantum mechanical Hamiltonians, which ...
Alberto Grünbaum +35 more
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