On the structure of tensor products of the finite-dimensional representations of quantum affine ${\mathfrak{s}\mathfrak{l}}_n$

We review some important facts about the structure of tensor products of finite dimensional representations of quantum affine algebras. This is done from the elementary standpoint of the representation theory of semisimple Lie algebras in the scope of a masters thesis. We set the focus on drawing the line to the finite dimensional representation theory of quantum affine ${\mathfrak{s}\mathfrak{l}}_n$, the theory of q-characters, and introduce the so called snake modules together with their character formula.