Some aspects of q- and qp-boson calculus
Résumé
A set of compatible formulas for the Clebsch-Gordan coefficients of the quantum algebra U_{q}({\rm su}_2) is given in this paper. These formulas are q-deformations of known formulas, as for instance: Wigner, van der Waerden, and Racah formulas. They serve as starting points for deriving various realizations of the unit tensor of U_{q}({\rm su}_2) in terms of q-boson operators. The passage from the one-parameter quantum algebra U_{q }({\rm su}_2) to the two-parameter quantum algebra U_{qp}({\rm u}_2) is discussed at the level of Clebsch-Gordan coefficients.