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General recurrence relations for Clebsch-Gordan coefficients of the quantum algebra \(U_ q(su_ 2)\). (English) Zbl 0742.33014

Summary: Two general recurrence relations for the Clebsch-Gordan coefficients of the quantum algebra \(U_ q(su_ 2)\), connecting their values for different meanings of the parameter \(\ell\) defining the representations, are derived. Recurrence formulas for the Racah coefficients of this algebra are given. Recurrence relations for the Racah coefficients of \(U_ q(su_ 2)\) are easily obtained from those for the classical Racah coefficients.

MSC:

33D80 Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics
17B37 Quantum groups (quantized enveloping algebras) and related deformations
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