Askey–Wilson relations and Leonard pairs [PDF]
Discrete Mathematics, 2008 22 pages; corrected version; the example of Section 2 has the normalization consistent with the rest of the ...
Vidunas, Raimundas
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Normalized Leonard pairs and Askey–Wilson relations [PDF]
Linear Algebra and its Applications, 2007 Let $V$ denote a vector space with finite positive dimension, and let $(A,B)$ denote a Leonard pair on $V$. As is known, the linear transformations $A,B$ satisfy the Askey-Wilson relations A^2B -bABA +BA^2 -g(AB+BA) -rB = hA^2 +wA +eI, B^2A -bBAB +AB^2 -h(AB+BA) -sA = gB^2 +wB +fI, for some scalars $b,g,h,r,s,w,e,f$.
Vidunas, Raimundas
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Higher Rank Relations for the Askey-Wilson and q-Bannai-Ito Algebra [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2019 The higher rank Askey-Wilson algebra was recently constructed in the $n$-fold tensor product of $U_q(\mathfrak{sl}_2)$. In this paper we prove a class of identities inside this algebra, which generalize the defining relations of the rank one Askey-Wilson algebra.
De Clercq, Hadewijch, De Clercq, H.
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Tridiagonal pairs and the Askey–Wilson relations [PDF]
Linear Algebra and its Applications, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nomura, Kazumasa, Kazumasa Nomura
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The structure relation for Askey–Wilson polynomials [PDF]
Journal of Computational and Applied Mathematics, 2007 An explicit structure relation for Askey-Wilson polynomials is given. This involves a divided q-difference operator which is skew symmetric with respect to the Askey-Wilson inner product and which sends polynomials of degree n to polynomials of degree n+1.
Koornwinder, Tom H. +2 more
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The Universal Askey-Wilson Algebra [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2011 In 1992 A. Zhedanov introduced the Askey-Wilson algebra AW=AW(3) and used it to describe the Askey-Wilson polynomials. In this paper we introduce a central extension Δ of AW, obtained from AW by reinterpreting certain parameters as central elements in ...
Paul Terwilliger
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Multi-indexed Wilson and Askey-Wilson polynomials [PDF]
, 2015 As the third stage of the project multi-indexed orthogonal polynomials, we present, in the framework of 'discrete quantum mechanics' with pure imaginary shifts in one dimension, the multi-indexed Wilson and Askey-Wilson polynomials.
Sasaki, Ryu, Odake, Satoru
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Contractions of 2D 2nd Order Quantum Superintegrable Systems and the Askey Scheme for Hypergeometric Orthogonal Polynomials [PDF]
, 2013 We show explicitly that all 2nd order superintegrable systems in 2 dimensions are limiting cases of a single system: the generic 3-parameter potential on the 2-sphere, S9 in our listing.
Willard Miller Jr. +8 more
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Multiple Askey–Wilson polynomials and related basic hypergeometric multiple orthogonal polynomials
Transactions of the American Mathematical Society, 2020 We first show how one can obtain Al-Salam--Chihara polynomials, continuous dual $q$-Hahn polynomials, and Askey--Wilson polynomials from the little $q$-Laguerre and the little $q$-Jacobi polynomials by using special transformations. This procedure is then extended to obtain multiple Askey--Wilson, multiple continuous dual $q$-Hahn, and multiple Al ...
Nuwacu, Jean Paul, Van Assche, Walter
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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]
Physics Letters B, 2009 7 pages; one reference added, published in Phys. Lett.
Odake, Satoru, Sasaki, Ryu
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