= SU(n) tensor transformation
{c}
{title2=$V^{\otimes j}\otimes(V^*)^{\otimes k}$}
A $(j,k)$ <tensor> has one <fundamental representation> factor for every upper index and a dual factor for every lower index. Under $A\in SU(n)$, upper factors transform by $A$ and lower factors by $A^{-1}$; unitarity identifies the latter with conjugate fundamental <matrices>. Thus <complex conjugation> exchanges $(j,k)$ and $(k,j)$. Index permutations and contraction with an <invariant tensor> commute with the action, producing <invariant subspaces> and decomposition maps.
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