Classical $$6j$$-symbols of finite-dimensional representations of the algebra $$\mathfrak{gl}_3$$
Dmitrii Vyacheslavovich Artamonov · Theoretical and Mathematical Physics · 2023
We find an explicit formula for an arbitrary $$6j$$ -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.