BGG reciprocity for current algebras

Abstract

It was conjectured by Bennett, Chari, and Manning that a BGG-type reciprocity holds for the category of graded representations with finite-dimensional graded components for the current algebra associated to a simple Lie algebra. We associate a current algebra to any indecomposable affine Lie algebra and show that, in this generality, the BGG reciprocity is true for the corresponding category of representations.

23 pg, corrections to Lemma 2.14

References in corpus (2)

• Current algebras, highest weight categories and quivers
• A uniform model for Kirillov-Reshetikhin crystals II. Alcove model, path model, and P=X

Cited by in corpus (21)

• Affine highest weight categories and affine quasihereditary algebras
• A uniform model for Kirillov-Reshetikhin crystals II. Alcove model, path model, and P=X
• Demazure character formula for semi-infinite flag varieties
• Modules with Demazure Flags and Character Formulae
• Reduced arc schemes for Veronese embeddings and global Demazure modules
• Frobenius splitting of Schubert varieties of semi-infinite flag manifolds
• Vertex algebras and coordinate rings of semi-infinite flags
• Beilinson-Drinfeld Schubert varieties and global Demazure modules
• Macdonald Polynomials and level two Demazure modules for affine ${\mathfrak{sl}}_{n+1}$
• Peter-Weyl, Howe and Schur-Weyl theorems for current groups
• Macdonald Polynomials and BGG reciprocity for current algebras
• A Weyl Module Stratification of Integrable Representations (with an appendix by Ryosuke Kodera)
• Nonsymmetric Rogers-Ramanujan sums and thick Demazure modules
• Tilting Modules in Truncated Categories
• Character formulae and a realization of tilting modules for ${\mathfrak{sl}}_2[t]$
• Positive level, negative level and level zero
• Generalized Weyl modules for twisted current algebras
• Tensor products of Kirillov-Reshetikhin modules and fusion products
• Symmetric functions and Springer representations
• Strands algebras and the affine highest weight property for equivariant hypertoric categories
• Trace and categorical sl(n) representations