Results 1 to 10 of about 2,985,600 (100)
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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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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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
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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
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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.
Terwilliger, Paul, Vidunas, Raimundas
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A conjecture concerning the q-Onsager algebra
Nuclear Physics B, 2021 The q-Onsager algebra Oq is defined by two generators W0,W1 and two relations called the q-Dolan/Grady relations. Recently Baseilhac and Kolb obtained a PBW basis for Oq with elements denoted{Bnδ+α0}n=0∞,{Bnδ+α1}n=0∞,{Bnδ}n=1∞. In their recent study of a
Paul Terwilliger
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A Linear Map Acts as a Leonard Pair with Each of the Generators of U(sl2)
International Journal of Mathematics and Mathematical Sciences, Volume 2020, Issue 1, 2020., 2020 Let ℱ denote an algebraically closed field with a characteristic not two. Fix an integer d ≥ 3; let x, y, and z be the equitable basis of sl2 over ℱ. Let V denote an irreducible sl2‐module with dimension d + 1; let A ∈ End(V). In this paper, we show that if each of the pairs A, x, A, y, and A, z acts on V as a Leonard pair, then these pairs are of ...
Hasan Alnajjar, Luca Vitagliano
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Physica D: Nonlinear Phenomena, 2022 We introduce three one-parameter semigroups of operators and determine their spectra. Two of them are fractional integrals associated with the Askey-Wilson operator. We also study these families as families of positive linear approximation operators. Applications include connection relations and bilinear formulas for the Askey-Wilson polynomials.
Ismail, Mourad E. H. +2 more
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A quadratic formula for basic hypergeometric series related to Askey-Wilson polynomials [PDF]
Proceedings of the American Mathematical Society, 2015 We prove a general quadratic formula for basic hypergeometric series, from which simple proofs of several recent determinant and Pfaffian formulas are obtained. A special case of the quadratic formula is actually related to a Gram determinant formula for Askey-Wilson polynomials. We also show how to derive a recent double-sum formula for the moments of
Zeng, Jiang +3 more
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Solutions to the Associated q-Askey-Wilson Polynomial Recurrence Relation [PDF]
, 1994 A $\tphin$ contiguous relation is used to derive contiguous relations for a very-well-poised $\ephis$. These in turn yield solutions to the associated $q$-Askey-Wilson polynomial recurrence relation, expressions for the associated continued fraction, the weight function and a $q$-analogue of a generalized Dougall's theorem.
Gupta, Dharma P., Masson, David R.
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