Wu-Ki Tung discusses the "tensorial approach" to deriving all the *finite* dimensional irreducible representations of GL(n, $\mathbb{C}$) in chapter 13 of his book Group Theory in Physics claiming that all those representations can be constructed from the standard/defining representation over $V$, its dual representation $V^*$, its complex conjugate representation $\overline{\ V}$ and its dual of the conjugate representation $\overline{\ V}^*$. My questions:

I. Are $\overline{\ V}$ and $\overline{\ V}^*$ really necessary?

II. How to reconcile this "tensorial approach" with the construction using the Schur functor (See, e.g., Representation Theory: A First Course by Fulton and Harris) applied to $V$ and/or $V^*$?

I know all finite dimensional irreducible linear representations can be realized as a subspace of the tensor product. In physics, people usually care about $\text{SO}(n)$ or $\text{SU}(n)$, so it really makes no difference.

I guess that I can find the answer if I have time to read Fulton and Harris' thoroughly, but unfortunately that is not feasible for the moment. I want to get the general picture, so I appreciate it if anyone can help.