I have been interested in representation theory lately in particular on that of Lie algebras. Now I have noticed that one way of building representations is to take tensor/exterior/symmetric powers. I have not studied multilinear algebra in depth before and I am looking for references on multilinear algebra relating to representation theory. I have had a look at Fulton and Harris and they do have an appendix section on this, but in the main text itself they seem to assume that the reader already has some prior knowledge of such material.
Can anyone recommend me any good references for methods of multilinear algebra in representation theory? In addition, what are common methods used to prove irreducibility of exterior/symmetric powers?
Edit: How much multilinear algebra is necessary in order to understand the ideas behind representation theory, such as symmetric and exterior powers of representations?