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On the triple sum formula for Wigner \(9j\)-symbols. (English) Zbl 0935.81036
Summary: The author gives a new proof of the triple sum formula for Wigner \(9j\)-symbols due to S. J. Ališauskas and A. P. Jucys [J. Math. Phys. 12, 594-605 (1971; Zbl 0214.28902)]. The proof uses explicit expressions for the coupling kernels recently introduced by the author [SIAM J. Math. Anal. 30, No. 2, 233-272 (1999)]. Parts of his results generalize to general recoupling coefficients.

MSC:
81R05 Finite-dimensional groups and algebras motivated by physics and their representations
20C35 Applications of group representations to physics and other areas of science
22E70 Applications of Lie groups to the sciences; explicit representations
33C80 Connections of hypergeometric functions with groups and algebras, and related topics
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