Results 1 to 10 of about 2,941 (107)
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_0^v,k_1^v;q) associated with the root system (C_1^v,C_1). We display three elements x, y, z in H that satisfy essentially the Z_3-symmetric Askey-Wilson relations.
Paul Terwilliger, Tatsuro Ito
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The Universal Askey-Wilson Algebra and DAHA of Type (C_1^∨,C_1) [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2013 Around 1992 A. Zhedanov introduced the Askey-Wilson algebra AW(3). Recently we introduced a central extension $Delta_q$ of AW(3) called the universal Askey-Wilson algebra.
Paul Terwilliger
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Hidden Symmetries of Stochastic Models [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2007 In the matrix product states approach to $n$ species diffusion processes the stationary probability distribution is expressed as a matrix product state with respect to a quadratic algebra determined by the dynamics of the process.
Boyka Aneva
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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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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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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 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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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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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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Recurrence Relations of the Multi-Indexed Orthogonal Polynomials : II [PDF]
, 2015 In a previous paper we presented $3+2M$ term recurrence relations with variable dependent coefficients for $M$-indexed orthogonal polynomials of Laguerre, Jacobi, Wilson and Askey-Wilson types.
Odake, Satoru
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Nonsymmetric Askey-Wilson polynomials as vector-valued polynomials [PDF]
, 2011 Nonsymmetric Askey-Wilson polynomials are usually written as Laurent polynomials. We write them equivalently as 2-vector-valued symmetric Laurent polynomials.
Chihara TS +5 more
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