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Generalized basic hypergeometric functions and the \(q\)-analogues of 3-\(j\) and 6-\(j\) coefficients. (English) Zbl 0751.33004

The authors study the relationship between basic hypergeometric functions and Racah and Clebsch-Gordan coefficients of the quantum algebra \(U_ q(sl_ 2)\). A lot of explicit expressions for these coefficients were derived earlier. The authors give new derivations for these coefficients. It is shown how properties of Racah and Clebsch-Gordan coefficients are related to those of the basic hypergeometric functions \(_ 4\phi_ 3\) and \(_ 3\phi_ 2\).
Reviewer: A.U.Klimyk (Kiev)

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
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
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