{"paper":{"title":"BGG reciprocity for current algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Matthew Bennett, Nathan Manning, Vyjayanthi Chari","submitted_at":"2011-06-02T00:19:18Z","abstract_excerpt":"We study the category $\\cal I_{\\gr}$ of graded representations with finite--dimensional graded pieces for the current algebra $\\lie g\\otimes\\bc[t]$ where $\\lie g$ is a simple Lie algebra. This category has many similarities with the category $\\cal O$ of modules for $\\lie g$ and in this paper, we formulate and study an analogue of the famous BGG duality. We recall the definition of the projective and simple objects in $\\cal I_{\\gr}$ which are indexed by dominant integral weights. The role of the Verma modules is played by a family of modules called the global Weyl modules. We show that in the c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0347","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}