I've start reading the part II (spin 1/2) of srednicki's qft book and I met a problem about group theory. In the section 34, the author describes the left and right handed spinor field.
He says that the hermitian conjugation swaps the two $SU(2)$ Lie algebras that comprise the Lie algebra of the Lorentz group, Therefore,the hermitian conjugate of a field in the $(2, 1)$ representation should be a field in the $(1, 2)$ representation (eq 34.11), but I can't understand this statement.
I think it's probably related to the fact that the generator of the two $SU(2)$ Lie algebra $N_i$ and $N_{i}^{\dagger}$ are conjugate to each other, but I don't know how deduce the conclusion that a field in the $(2,1)$ representation will become a field in $(1,2)$ representation after a hermitian conjugation from this.
