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Some Aspects of $q$- and $qp$-Boson Calculus

M. R. Kibler·R. M. Asherova·Yu. F. Smirnov
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Abstract

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.

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M. R. Kibler, R. M. Asherova, Yu. F. Smirnov. 1994-12-09. Some Aspects of $q$- and $qp$-Boson Calculus. https://arxiv.org/abs/hep-th/9412082

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