Given some chiral conformal field theory (also known as a vertex operator algebra in the mathematics literature), a natural but highly non-trivial task is to classify its representation theory. In this talk, I will use some well known examples of conformal field theories, such as the Virasoro minimal models, to show how certain hard questions in representation theory can be neatly rephrased as comparatively easy questions in the theory of symmetric polynomials. After a brief overview of the theory of symmetric polynomials, I will show how they can be used to classify irreducible representations.