Results 11 to 20 of about 901,840 (78)
Contractions of 2D 2nd Order Quantum Superintegrable Systems and the Askey Scheme for Hypergeometric Orthogonal Polynomials [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2013 We show explicitly that all 2nd order superintegrable systems in 2 dimensions are limiting cases of a single system: the generic 3-parameter potential on the 2-sphere, S9 in our listing.
Ernest G. Kalnins +2 more
doaj +2 more sources
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
doaj +2 more sources
Raising and Lowering Operators for Askey-Wilson Polynomials
Symmetry, Integrability and Geometry: Methods and Applications, 2007 In this paper we describe two pairs of raising/lowering operators for Askey-Wilson polynomials, which result from constructions involving very different techniques. The first technique is quite elementary, and depends only on the ''classical'' properties
Siddhartha Sahi
doaj +1 more source
Multi-indexed Wilson and Askey-Wilson polynomials [PDF]
, 2015 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.
Sasaki, Ryu, Odake, Satoru
core +2 more sources
Vanishing Results for Hall-Littlewood Polynomials [PDF]
, 2012 It is well-known that if one integrates a Schur function indexed by a partition λ over the symplectic (resp. orthogonal) group, the integral vanishes unless all parts of λ have even multiplicity (resp. all parts of λ are even).
Venkateswaran, Vidya
core +1 more source
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.
Tom H. Koornwinder +4 more
core +1 more source
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
On Some Limit Cases of Askey–Wilson Polynomials [PDF]
, 1998 We show that limit transitions from Askey–Wilson polynomials toq-Racah, little and bigq-Jacobi polynomials can be made rigorous on the level of their orthogonality measures in a suitable weak sense.
Stokman, J.V. +2 more
core +1 more source
Exceptional Askey-Wilson type polynomials through Darboux-Crum transformations [PDF]
, 2010 An alternative derivation is presented of the infinitely many exceptional Wilson and Askey-Wilson polynomials, which were introduced by the present authors in 2009.
Sasaki R +7 more
core +2 more sources