In "Quantum Field Theory in a Nutshell" pg424 the author (Zee) writes:
$$(n\oplus n^*)\otimes_A(n \oplus n^*)\quad\cong\quad(n^2-1)\oplus 1 \oplus n(n-1)/2 \oplus ((n(n-1))/2)^*$$
From what I understand to do the $n\otimes_A n$ we look at the contractions with the Levi-Civita tensor e.g. in SU(3) $$3\otimes_A 3=\varepsilon^{ijk}\psi_i\phi_j=3^*$$ but I don't understand how to do the same for $(n \otimes_A n^*)\oplus(n^* \otimes_A n)$ to get the adjoint (if it is actually the adjiont and not some anti-symmetric version?) and singlet reps. Please can someone explain?
Note: I have recently have being asking similar questions on MSE but apparently the notation used here is only common in physics - that along with its relations to the standard model I thought it was best to post this one here.