TITLE: Reference on Highest Weight Module of Kac-Moody Algebra
QUESTION [6 upvotes]: 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.

REPLY [4 votes]: I highly recommend the book
 Affine Lie Algebras, Weight Multiplicities, and Branching Rules
by Kass, Moody, Patera, and Slansky.
https://www.ucpress.edu/op.php?isbn=9780520067684