LOGARITHMIC CONFORMAL FIELD THEORY: BEYOND AN INTRODUCTION
another source for defining Loewy diagrams (this one by Rupert's advisor Creutzig) since all three of the previous papers are kinda vague about when to draw arrows in Loewy diagrams (this one is also a little bit vague, but you can figure it out by comparing the definitions in the different papers)
Representations of Semisimple Lie Algebras in the BGG Category O
Not fully necessary, but seems to be a nice self contained book that covers the classical version of a lot of the theory being used i.e. standard filtrations, BGG reciprocity, Kazhdan Lusztig Conjecture, etc