{"paper":{"title":"Prime Representations from a Homological Perspective","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Adriano Moura, Charles Young, Vyjayanthi Chari","submitted_at":"2011-12-29T18:59:59Z","abstract_excerpt":"We begin the study of simple finite-dimensional prime representations of quantum affine algebras from a homological perspective. Namely, we explore the relation between self extensions of simple representations and the property of being prime. We show that every nontrivial simple module has a nontrivial self extension. Conversely, if a simple representation has a unique nontrivial self extension up to isomorphism, then its Drinfeld polynomial is a power of the Drinfeld polynomial of a prime representation. It turns out that, in the sl(2) case, a simple module is prime if and only if it has a u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.6376","kind":"arxiv","version":1},"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"}