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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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Extended commutator algebra for the $q$-oscillator and a related Askey-Wilson algebra
Communications in Mathematics, 2023 Let $q$ be a nonzero complex number that is not a root of unity. In the $q$-oscillator with commutation relation $ a a^+-qa^+ a =1$, it is known that the smallest commutator algebra of operators containing the creation and annihilation operators $a^+$ and $ a $ is the linear span of $a^+$ and $ a $, together with all operators of the form ${a^+}^l ...
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The Universal Askey-Wilson Algebra and DAHA of Type (C_1^∨,C_1)
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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Advances in Mathematical Physics, Volume 2009, Issue 1, 2009., 2009 In this paper, we apply to (almost) all the “named” polynomials of the Askey scheme, as defined by their standard three‐term recursion relations, the machinery developed in previous papers. For each of these polynomials we identify at least one additional recursion relation involving a shift in some of the parameters they feature, and for several of ...
M. Bruschi +3 more
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The dynamical U(n) quantum group
International Journal of Mathematics and Mathematical Sciences, Volume 2006, Issue 1, 2006., 2006 We study the dynamical analogue of the matrix algebra M(n), constructed from a dynamical R‐matrix given by Etingof and Varchenko. A left and a right corepresentation of this algebra, which can be seen as analogues of the exterior algebra representation, are defined and this defines dynamical quantum minor determinants as the matrix elements of these ...
Erik Koelink, Yvette Van Norden
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Multivariable q‐Hahn polynomials as coupling coefficients for quantum algebra representations
International Journal of Mathematics and Mathematical Sciences, Volume 28, Issue 6, Page 331-358, 2001., 2001 We study coupling coefficients for a multiple tensor product of highest weight representations of the SU(1, 1) quantum group. These are multivariable generalizations of the q‐Hahn polynomials.
Hjalmar Rosengren
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Journal of Advanced Research, 2010 Formulae expressing explicitly the q-difference derivatives and the moments of the polynomials Pn(x ; q) ∈ T (T ={Pn(x ; q) ∈ Askey–Wilson polynomials: Al-Salam-Carlitz I, Discrete q-Hermite I, Little (Big) q-Laguerre, Little (Big) q-Jacobi, q-Hahn ...
Eid H. Doha, Hany M. Ahmed
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A characterization of the Rogers q‐hermite polynomials
International Journal of Mathematics and Mathematical Sciences, Volume 18, Issue 4, Page 641-647, 1995., 1994 In this paper we characterize the Rogers q‐Hermite polynomials as the only orthogonal polynomial set which is also 𝒟q‐Appell where 𝒟q is the Askey‐Wilson finite difference operator.
Waleed A. Al-Salam
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On the Askey--Wilson type integrals [PDF]
, 2023 The Askey--Wilson integral is very important in the theory of orthogonal polynomials. Liu's integral is a generalization of the Askey--Wilson integral with many parameters. With the help of the series rearrangement method, we give the elementary proof of
Wei, Chuanan
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A Whittaker-Shannon-Kotelnikov sampling theorem related to the Askey-Wilson functions [PDF]
Journal of Nonlinear Mathematical Physics, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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