= Real structure of the SU4 exterior square
{title2=$(\mathcal JT)^{ab}=\tfrac12\epsilon^{abcd}\overline{T^{cd}},\quad\mathcal J^2=1$}
On $\bigwedge^2\mathbb C^4$, the invariant Hermitian form and volume <tensor> define the displayed <antilinear map> with square one, commuting with <SU(4)>. Its fixed space satisfies $T^{12}=\overline{T^{34}}$, $T^{13}=-\overline{T^{24}}$, and $T^{14}=\overline{T^{23}}$. Three complex choices give six real coordinates, and this fixed space has the original exterior square as its complexification. It is therefore a <real representation> of dimension six, rather than merely the twelve-dimensional realification of an arbitrary six-dimensional complex representation.
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