This sales pitch is loosely based on a paper of Barcelo and Ram (http://arxiv.org/abs/math/9707221), in which they attempt to describe the desired aesthetic of a result in combinatorial representation theory. I will do my best to communicate this aesthetic to you through two examples: the finite-dimensional representations of the symmetric groups, and the polynomial representations of GL(n,k) for k an algebraically closed field of characteristic zero. As it turns out, there is a nice combinatorial description of each theory. If time permits, I also hope to describe the relationship between the two examples using the language of polynomial functors.
What Makes Representation Theory Combinatorial ?