= Exterior square of the sl3 representation of highest weight (2,1)
{title2=$\bigwedge^2\Gamma_{2,1}\cong\Gamma_{5,0}\oplus\Gamma_{2,3}\oplus\Gamma_{3,1}\oplus\Gamma_{1,2}\oplus\Gamma_{0,1}$}
The <formal character> identity $\chi_{\wedge^2U}(x)=\tfrac12(\chi_U(x)^2-\chi_U(x^2))$ counts unordered pairs of distinct basis vectors. Substituting $\chi_{2,1}=h_2(x)h_1(x^{-1})-h_1(x)$ and the <Weyl character formula> gives the displayed multiplicity-free decomposition. Its dimensions sum to $21+42+24+15+3=105=\binom{15}{2}$. The <sl3 interlacing character formula> provides an exact weight-enumeration check.
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