= Mixed SU(3) tensor representation
{title2=$V^{\otimes k}\otimes(V^*)^{\otimes l}$}
A mixed <tensor> has $k$ defining indices and $l$ dual indices. The <SU(3)> action applies $U$ to every upper index and $U^{-1}$ to every lower index. <Young symmetrizers> select permutation types, while invariant <Kronecker deltas> take <traces> and invariant alternating <tensors> convert an antisymmetric pair of defining indices into a dual index, or conversely. Repeated fundamental and dual <tensor> rules decompose it with multiplicities: $(p,q)\otimes(1,0)=(p+1,q)\oplus(p-1,q+1)\oplus(p,q-1)$ and the conjugate rule, omitting negative labels.
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