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In short (just the dimensions): $6\cdot6=1+1+6+8+8+12$. Does a Lie group expert recognize that pattern?
What's fishy is the second "$1$" (is that allowed by Schur's Lemma if it's an "antisymmetric $1$"?). But otherwise, it looks perfectly like a quantum group derived expansion - the "$6$" comes from quantum dimension $2(1+q^2+1/q^2)$, it has a proper R matrix and a proper rank-$3$ tensor (on request if that helps, longformula is loooooong :-) Oh, and the $6j$ symbol $\{6\ 6\ 6 \mid 6\ 6\ 6\}$ vanishes.

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