Results 11 to 20 of about 3,132,788 (112)
Askey-Wilson braid algebra and centralizer of $U_q(\mathfrak{sl}_2)$ [PDF]
, 2022 A presentation of the centralizer of the three-fold tensor product of the spin $s$ representation of the quantum group $U_q(\mathfrak{sl}_2)$ is provided. It is expressed as a quotient of the Askey-Wilson braid algebra.
d'Andecy, Loic Poulain +8 more
core +1 more source
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
doaj +1 more source
On First type characterizations of Askey-Wilson polynomials [PDF]
, 2023 In this chapter we characterize Askey-Wilson polynomials including specific and limiting cases of them by some structure relations of the first type.Comment: arXiv admin note: text overlap with arXiv:2301 ...
Mbouna, D., Suzuki, A.
core +1 more source
A Linear Map Acts as a Leonard Pair with Each of the Generators of U(sl2)
International Journal of Mathematics and Mathematical Sciences, Volume 2020, Issue 1, 2020., 2020 Let ℱ denote an algebraically closed field with a characteristic not two. Fix an integer d ≥ 3; let x, y, and z be the equitable basis of sl2 over ℱ. Let V denote an irreducible sl2‐module with dimension d + 1; let A ∈ End(V). In this paper, we show that if each of the pairs A, x, A, y, and A, z acts on V as a Leonard pair, then these pairs are of ...
Hasan Alnajjar, Luca Vitagliano
wiley +1 more source
Physica D: Nonlinear Phenomena, 2022 We introduce three one-parameter semigroups of operators and determine their spectra. Two of them are fractional integrals associated with the Askey-Wilson operator. We also study these families as families of positive linear approximation operators. Applications include connection relations and bilinear formulas for the Askey-Wilson polynomials.
Ismail, Mourad E. H. +2 more
openaire +3 more sources
A quadratic formula for basic hypergeometric series related to Askey-Wilson polynomials [PDF]
Proceedings of the American Mathematical Society, 2015 We prove a general quadratic formula for basic hypergeometric series, from which simple proofs of several recent determinant and Pfaffian formulas are obtained. A special case of the quadratic formula is actually related to a Gram determinant formula for Askey-Wilson polynomials. We also show how to derive a recent double-sum formula for the moments of
Zeng, Jiang +3 more
openaire +3 more sources
Solutions to the Associated q-Askey-Wilson Polynomial Recurrence Relation [PDF]
, 1994 A $\tphin$ contiguous relation is used to derive contiguous relations for a very-well-poised $\ephis$. These in turn yield solutions to the associated $q$-Askey-Wilson polynomial recurrence relation, expressions for the associated continued fraction, the weight function and a $q$-analogue of a generalized Dougall's theorem.
Gupta, Dharma P., Masson, David R.
openaire +2 more sources
The Askey-Wilson algebra and its avatars [PDF]
, 2021 The original Askey-Wilson algebra introduced by Zhedanov encodes the bispectrality properties of the eponym polynomials. The name 'Askey-Wilson algebra' is currently used to refer to a variety of related structures that appear in a large number of ...
Frappat, Luc +12 more
core +1 more source
Contractions of 2D 2nd Order Quantum Superintegrable Systems and the Askey Scheme for Hypergeometric Orthogonal Polynomials [PDF]
, 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.
Willard Miller Jr. +8 more
core +1 more source
Multiple Askey–Wilson polynomials and related basic hypergeometric multiple orthogonal polynomials
Transactions of the American Mathematical Society, 2020 We first show how one can obtain Al-Salam--Chihara polynomials, continuous dual $q$-Hahn polynomials, and Askey--Wilson polynomials from the little $q$-Laguerre and the little $q$-Jacobi polynomials by using special transformations. This procedure is then extended to obtain multiple Askey--Wilson, multiple continuous dual $q$-Hahn, and multiple Al ...
Nuwacu, Jean Paul, Van Assche, Walter
openaire +3 more sources