Geodesic
Classical $6j$-symbols of finite-dimensional representations of the~algebra $\mathfrak{gl}_3$
Teoretičeskaâ i matematičeskaâ fizika, Tome 216 (2023) no. 1, pp. 3-19

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We find anЁexplicit formula for anЁarbitrary $6j$-symbol of finite-dimensional irreducible representations of the Lie algebra $\mathfrak{gl}_3$. It is given by the result of substituting $\pm 1$s in a hypergeometric-type series similar to the $\Gamma$-series, which is the simplest several-variate hypergeometric series. We present necessary conditions for the $6j$-symbol to be nonzero.
Keywords: $6j$-symbols, hypergeometric functions. 
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     title = {Classical $6j$-symbols of finite-dimensional representations of the~algebra $\mathfrak{gl}_3$},
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D. V. Artamonov. Classical $6j$-symbols of finite-dimensional representations of the~algebra $\mathfrak{gl}_3$. Teoretičeskaâ i matematičeskaâ fizika, Tome 216 (2023) no. 1, pp. 3-19. http://geodesic.mathdoc.fr/item/TMF_2023_216_1_a0/