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We construct a set of Wigner 6j symbols with gluon lines (adjointrepresentations) in closed form, expressed in terms of similar 6j symbols withquark lines (fundamental representations). Together with Wigner 6j symbols withquark lines, this gives a set of 6j symbols sufficient for treating QCD colorstructure for any number of external particles, in or beyond perturbationtheory. This facilitates a complete treatment of QCD color structure in termsof orthogonal multiplet bases, without the need of ever explicitly constructingthe corresponding bases. We thereby open up for a completely representationtheory based treatment of SU(N) color structure, with the potential ofsignificantly speeding up the color structure treatment.

Wigner 6j symbols with gluon lines: completing the set of 6j symbols required for color decomposition