Classical $6j$-symbols for finite dimensional representation of the algebra ${\mathfrak{gl}}_3$

Abstract

In the paper an explicit formula for an arbitrary $6j$-symbol for finite-dimensional irreducible representations of the algebra ${\mathfrak{gl}}_3$ is derived. A $6j$-symbol is written as a result of substitution of $\pm 1$ into a series of hypergeometric type, which is similar to a $\Gamma$-series, which is a simplest example of a multivariate series of hypergeometric type. The selection rulers for a $6j$-symbol are derived.

21 pages; several typos are corrected

References in corpus (3)

• Multiplicity-free $U_q(s{l}_N)$ 6-j symbols: relations, asymptotics, symmetries
• On $6j$-symbols for symmetric representations of $U_q({\mathfrak{su}}_N)$
• $3j$-symbols for representation of the Lie algebra ${\mathfrak{gl}}_3$ in the Gelfand-Tselin base

Cited by in corpus (1)

• Calculation of $6j$-symbols for the Lie algebra ${\mathfrak{gl}}_n$