Let us return to our case. We want to demonstrate that there are no excitations transforming in the adjoint of . So, we consider the special case of Frobenius reciprocity when is the adjoint rep of .

We have to go over all the tensor representations and verify if enters into using Eq. (5). We observe:

(the decomposition of as a rep of ) Now Eq. (5) reads:

[antisymm. tensors]