Calculation of $6j$-symbols for the Lie algebra glₙ

We give an explicit description of the multiplicity space that describes an occurence of a certain irreducible representation into a splitting of a tensor product of two irreducible representations of glₙ. Using this descripition an explicit formula for an arbitrary $6j$-symbol for the algebra glₙ is derived. It is expressed through a value of a generalized hypergeometric function.