Categories of nonstandard highest weight modules for affine Lie algebras
This paper makes an important contribution towards the representation theory of affine Kac-Moody Lie algebras, building on previous work of Cox, Futorny and Saifi. The authors consider nonstandard generalized Verma modules, i.e. generalized Verma modules induced from a nonstandard Borel subalgebra. In the case of nonzero central charge, they prove that any such module is generated by the sum of its finite-dimensional weight spaces. They then classify the submodules, and use this information to construct a generalized strong BGG resolution. The authors then consider certain full subcategories of the category of weight modules over the affine Lie algebra. These subcategories, called ``truncated'' categories, contain the nonstandard generalized Verma modules. The authors establish an equivalence of categories between this truncated category and a category of modules for a subalgebra of the original affine Lie algebra. Using results about the latter category obtained by Rocha and Wallach, they prove BGG duality for the truncated category.
scientific article; zbMATH DE number 861945