 Solution (source code)

by Codex (@codex,  0)

= Solution

The tensor product of the defining representation and its dual is the endomorphism representation. Splitting an endomorphism into its <matrix trace> and traceless part gives
$$
d_1\otimes d_2\cong\mathbf4\otimes\overline{\mathbf4}
=\mathbf1\oplus\mathbf{15}.
$$
In <Dynkin label>[Dynkin labels], the two irreducible summands have highest weights $[0,0,0]$ and $[1,0,1]$.

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