Representations and Clebsch-Gordan coefficients for the Jordanian quantum algebra

Representations of the Lie algebra ĝl ∞ and “ reciprocity formula ” for Clebsch – Gordan coefficients

Jordanian Deformation of Su(2) 1 the Jordanian Deformation of Su(2) and Clebsch-gordan Coefficients †

Representation theory for the Jordanian quantum algebra Uh(sl(2)) is developed using a nonlinear relation between its generators and those of sl(2). Closed form expressions are given for the action of the generators of Uh(sl(2)) on the basis vectors of finite dimensional irreducible representations. In the tensor product of two such representations, a new basis is constructed on which the gener...

Su(3) Clebsch-gordan Coefficients

The purpose of this paper is to find out a set of general recurrence formulas for the calculus of the SU(3) Clebsch-Gordan coefficients. The first six sections are introductory, presenting the notations and general group theoretical methods applied to SU(3). The following eight sections are devoted to a detailed treatment of the carrier spaces of the irreducible representations and their direct...

2 00 1 Clebsch - Gordan coefficients and the binomial distribution

There appear to be two standard ways of calculation C-G coefficients in quantum mechanics. One method is to combine the “ladder” operator approach with orthogonality conditions. The second method is to use some type of closed form [2] which allows the coefficients to be calculated directly. However, the latter approach is at times considered “tedious” [2] and does not reveal any new information...

Hidden Symmetry of the Racah and Clebsch - Gordan Problems for the Quantum Algebra

The Askey-Wilson algebra AW (3) with three generators is shown to serve as a hidden symmetry algebra underlying the Racah and (new) generalized Clebsch-Gordan problems for the quantum algebra sl q (2). On the base of this hidden symmetry a simple method to calculate corresponding coefficients in terms of the Askey-Wilson polynomials is proposed.