A NEW MODULE CATEGORY FOR BRST REDUCTION IN THE REPRESENTATION THEORY OF AFFINE LIE SUPERALGEBRAS

We introduce a new category of modules over affine Lie (super)algebras, based on quasi highest weight modules, motivated by the necessity for a duality-stable and homologically well-behaved class of representations in the context of BRST reduction. We demonstrate that this category is the smallest full subcategory of affine Lie (super)algebra modules that contains quasi highest weight modules and is closed under finite direct sums and duals.