DOI10.1137/S003614109630673XzbMath0977.33013arXivq-alg/9607010OpenAlexW2021292163WikidataQ115246838 ScholiaQ115246838MaRDI QIDQ4389043
H. T. Koelink, Joris Van der Jeugt
Publication date: 11 May 1998
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/q-alg/9607010
Quantum groups (quantized enveloping algebras) and related deformations (17B37)
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45)
Connections of hypergeometric functions with groups and algebras, and related topics (33C80)
Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45)
Simple, semisimple, reductive (super)algebras (17B20)
Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)
Introduction to Leonard pairs.,
Expansion formulas for terminating balanced \(_{4} F_{3}\)-series from the Biedenharn--Elliot identity for \(\mathfrak{su}(1,1)\),
An elementary approach to \(6j\)-symbols (classical, quantum, rational, trigonometric, and elliptic),
Some systems of multivariable orthogonal \(q\)-Racah polynomials,
The non-compact XXZ spin chain as stochastic particle process,
Generalized Burchnall-type identities for orthogonal polynomials and expansions,
Intertwiners of $U^{\prime }_q\bigl (\widehat{sl}(2)\bigr )$Uq′sl̂(2)-representations and the vector-valued big q-Jacobi transform,
Coupling coefficients for tensor product representations of quantum SU(2),
Global Asymptotics for Meixner-Pollaczek Polynomials with a Varying Parameter,
3nj-coefficients of su(1,1) as connection coefficients between orthogonal polynomials in n variables,
Little and big \(q\)-Jacobi polynomials and the Askey-Wilson algebra,
Quasinormal modes from Penrose limits,
Orthogonal functions related to Lax pairs in Lie algebras,
Fourier transforms of some special functions in terms of orthogonal polynomials on the simplex and continuous Hahn polynomials,
Realisations of Racah algebras using Jacobi operators and convolution identities,
Doubling (dual) Hahn polynomials: classification and applications,
Identities for Rankin-Cohen brackets, Racah coefficients and associativity,
Two-dimensional Meixner random vectors of class \({\mathcal{M}}_{L}\),
Coupling coefficients of \(\operatorname{su}_{q}(1,1)\) and multivariate \(q\)-Racah polynomials,
An Askey-Wilson algebra of rank 2,
Realizations of coupled vectors in the tensor product of representations of \(\mathfrak{su}(1,1)\) and \(\mathfrak{su}(2)\),
Transmutation kernels for the little \(q\)-Jacobi function transform.,
Leonard pairs from 24 points of view.,
Volterra-type convolution of classical polynomials,
Laguerre functions and representations of \(su\)(1,1),
Inequalities for zeros of Jacobi polynomials via Obrechkoff’s theorem,
Orthogonal stochastic duality functions from Lie algebra representations,
Tensor products of $U^{\prime }_q\bigl (\widehat{sl}(2)\bigr )$Uq′sl̂(2)-modules and the big q2-Jacobi function transform,
Free Meixner states,
New realizations of algebras of the Askey–Wilson type in terms of Lie and quantum algebras,
The oscillator model for the Lie superalgebra $\mathfrak {sh}(2|2)$sh(2|2) and Charlier polynomials,
Connection coefficients for classical orthogonal polynomials of several variables,
Convolutions and zeros of orthogonal polynomials,
LEONARD PAIRS AND THE ASKEY–WILSON RELATIONS,
Wilson function transforms related to Racah coefficients,
Generating function for the Bannai-Ito polynomials,
Self-duality of Markov processes and intertwining functions,
Realizations of su(1,1) and Uq(su(1,1)) and generating functions for orthogonal polynomials,
Heun algebras of Lie type,
Convolution identities for Dunkl orthogonal polynomials from the osp(1|2) Lie superalgebra,
Hypergeometric series related to the \(9-j\) coefficient of \({\mathfrak{su}}(1,1)\),
A \(q\)-analogue of the 9-\(j\) symbols and their orthogonality,
Asymptotic approximations of the continuous Hahn polynomials and their zeros,
Two linear transformations each tridiagonal with respect to an eigenbasis of the other; the TD-D canonical form and the LB-UB canonical form,
Wigner quantization of some one-dimensional Hamiltonians,
A bispectral q-hypergeometric basis for a class of quantum integrable models
