1. The problem statement, all variables and given/known data (a) For SU(N), we have: N ⊗ N = A_A + S_S where A corresponds to a field with two antisymetric fundamental SU(N) in- dices φij = −φji, and S corresponds to a field with two symmetric fundamental SU(N) indices φij = φji. By considering an SU(2) subgroup of SU(N), compute T(A) and T(S). 2. Relevant equations Under the SU(2) subgroup, N transforms as: [2 ⊕ (N − 2)1S] ⊗ [2 ⊕ (N − 2)1s] = A + S. 3. The attempt at a solution Distributing, we get, among other terms, 2 ⊗ (N − 2)1S ⊕ 2 ⊗ (N − 2)1S. It's then just a matter of separating the symmetric and anti-symmetric terms. What I don't understand is why one of these 2 ⊗ (N − 2)1S terms is symmetric and the otherone is anti-symmetric. They seem identical to me..... I think part of the problem is I don't understand Srednicki's notation 1s (sometimes 1's) -- does this just mean the singlet is symmetrical? I understand Young Tableaux, but not sure how to use them here, the only diagram I can work out is adjoint, and therefore neither symmetrical nor anti-symmetrical. This is the only difficulty, if we can figure out this, I know how to solve the problem from there..... Thanks!