Results 21 to 30 of about 2,941 (107)

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 ...
openaire   +4 more sources

Additional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme

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, F. Calogero, R. Droghei, M. Lakshmanan   +3 more
wiley   +1 more source

Higher Rank Relations for the Askey-Wilson and q-Bannai-Ito Algebra [PDF]

Symmetry, Integrability and Geometry: Methods and Applications, 2019
The higher rank Askey-Wilson algebra was recently constructed in the $n$-fold tensor product of $U_q(\mathfrak{sl}_2)$. In this paper we prove a class of identities inside this algebra, which generalize the defining relations of the rank one Askey-Wilson algebra.
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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
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

Efficient algorithms for construction of recurrence relations for the expansion and connection coefficients in series of quantum classical orthogonal polynomials

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
doaj   +1 more source

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.
openaire   +1 more source

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
wiley   +1 more source

The higher rank $q$-deformed Bannai-Ito and Askey-Wilson algebra [PDF]

, 2019
The $q$-deformed Bannai-Ito algebra was recently constructed in the threefold tensor product of the quantum superalgebra $\mathfrak{osp}_q(1\vert 2)$. It turned out to be isomorphic to the Askey-Wilson algebra.
De Bie, Hendrik, De Clercq, Hadewijch, van de Vijver, Wouter   +2 more
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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
doaj   +1 more source