I am trying to understand this paper. The construction requires the understanding of the following concepts in the representation theory of simple and affine Lie algebras:

• The construction of Verma module for a general (not necessarily integral) highest-weight state;
• The character for these modules (the Weyl-Kac character formula cannot be applied for a generic non-integral highest-weight module);
• BRST reduction of affine Lie algebras;
• Quantum Drinfeld-Sokolov reduction;
• ...

I am looking for some references that explain these concepts or some detailed examples of the construction for simplest cases. I appreciate any comment.