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Askey–Wilson Relations and Leonard Pairs
Discrete Mathematics, 2008 22 pages; corrected version; the example of Section 2 has the normalization consistent with the rest of the ...
Raimundas Vidunas
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Leonard Pairs and the Askey–Wilson Relations [PDF]
Journal of Algebra and Its Applications, 2004 Let K denote a field and let V denote a vector space over K with finite positive dimension. We consider an ordered pair of linear transformations A:V→V and A*:V→V which satisfy the following two properties:(i) There exists a basis for V with respect to which the matrix representing A is irreducible tridiagonal and the matrix representing A* is diagonal.
Raimundas Vidunas, Paul M. Terwilliger
exaly +3 more sources
Normalized Leonard pairs and Askey–Wilson relations
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
core +4 more sources
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.
openaire +4 more sources
Chern–Simons theory, link invariants and the Askey–Wilson algebra
Nuclear Physics B, 2022 The occurrence of the Askey–Wilson (AW) algebra in the SU(2) Chern–Simons (CS) theory and in the Reshetikhin–Turaev (RT) link invariant construction with quantum algebra Uq(su2) is explored.
Nicolas Crampé, Luc Vinet, Meri Zaimi
doaj +2 more sources
The structure relation for Askey–Wilson polynomials
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, T.H.; id_orcid
openaire +6 more sources
Diagonalization of the Heun-Askey-Wilson operator, Leonard pairs and the algebraic Bethe ansatz [PDF]
Nuclear Physics B, 2019 An operator of Heun-Askey-Wilson type is diagonalized within the framework of the algebraic Bethe ansatz using the theory of Leonard pairs. For different specializations and the generic case, the corresponding eigenstates are constructed in the form of ...
Pascal Baseilhac, Rodrigo A. Pimenta
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Double Affine Hecke Algebras of Rank 1 and the Z 3 -Symmetric Askey-Wilson Relations [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2010 We consider the double affine Hecke algebra $H=H(k_0,k_1,k^\vee_0,k^\vee_1;q)$ associated with the root system $(C^\vee_1,C_1)$. We display three elements $x$, $y$, $z$ in $H$ that satisfy essentially the $Z_3$-symmetric Askey-Wilson relations. We obtain the relations as follows.
Paul Terwilliger, Tatsuro Ito
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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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Discrete Analogues of the Erdélyi Type Integrals for Hypergeometric Functions
Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022 Gasper followed the fractional calculus proof of an Erdélyi integral to derive its discrete analogue in the form of a hypergeometric expansion. To give an alternative proof, we derive it by following a procedure analogous to a triple series manipulation‐based proof of the Erdélyi integral, due to “Joshi and Vyas”. Motivated from this alternative way of
Yashoverdhan Vyas +5 more
wiley +1 more source