Affine Lie algebra representation for minimal model holography

Question

Look at the first few pages (say till page 6) of this paper, http://arxiv.org/abs/1310.1744

It seems to assume quite a bit of understanding of the results on representation theory of $su(N)_k$.

Can someone give a reference from where one can pick up this background mathematics quickly enough?

Answer 1

The book by Fuchs and Schweigert is probably a good starting point.