Results 31 to 40 of about 442,685 (123)
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
wiley +1 more source
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
wiley +1 more source
Orthogonal Basic Hypergeometric Laurent Polynomials
Symmetry, Integrability and Geometry: Methods and Applications, 2012 The Askey-Wilson polynomials are orthogonal polynomials in$x = cos heta$, which are given as a terminating $_4phi_3$ basic hypergeometric series. The non-symmetric Askey-Wilson polynomials are Laurent polynomials in $z=e^{iheta}$, which are given as a ...
Mourad E.H. Ismail, Dennis Stanton
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On Solutions of Holonomic Divided-Difference Equations on Nonuniform Lattices
Axioms, 2013 The main aim of this paper is the development of suitable bases that enable the direct series representation of orthogonal polynomial systems on nonuniform lattices (quadratic lattices of a discrete or a q-discrete variable). We present two bases of this
Salifou Mboutngam +3 more
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Bispectrality of the Complementary Bannai-Ito Polynomials
Symmetry, Integrability and Geometry: Methods and Applications, 2013 A one-parameter family of operators that have the complementary Bannai-Ito (CBI) polynomials as eigenfunctions is obtained. The CBI polynomials are the kernel partners of the Bannai-Ito polynomials and also correspond to a q→−1 limit of the Askey-Wilson ...
Vincent X. Genest +2 more
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Multivariable Askey-Wilson Polynomials and Quantum Complex Grassmannians [PDF]
, 1996 We present a one-parameter family of constant solutions of the reflection equation and define a family of quantum complex Grassmannians endowed with a transitive action of the quantum unitary group.
M. Noumi, M. Dijkhuizen, T. Sugitani
semanticscholar +1 more source
The Universal Askey-Wilson Algebra
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]
, 2012 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.
S. Odake, R. Sasaki
semanticscholar +1 more source
On the Limit from q-Racah Polynomials to Big q-Jacobi Polynomials
Symmetry, Integrability and Geometry: Methods and Applications, 2011 A limit formula from q-Racah polynomials to big q-Jacobi polynomials is given which can be considered as a limit formula for orthogonal polynomials.
Tom H. Koornwinder
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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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