= sl3 highest-weight tensor rule
{title2=$\Gamma_{a,b}\otimes\Gamma_{1,0}\cong\Gamma_{a+1,b}\oplus\Gamma_{a-1,b+1}\oplus\Gamma_{a,b-1}$}
For the complex <special linear Lie algebra> $\mathfrak{sl}_3$, tensoring an irreducible <highest-weight representation> by the defining representation gives the displayed sum, omitting terms with negative <Dynkin labels>. It follows by multiplying its <Weyl character formula> by $x_1+x_2+x_3$. In particular $\Gamma_{2,1}\otimes\Gamma_{1,0}=\Gamma_{3,1}\oplus\Gamma_{1,2}\oplus\Gamma_{2,0}$, with dimensions $24+15+6=45$.
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