{"paper":{"title":"Parabolic sheaves on surfaces and affine Lie algebra $\\hat{gl}_n$","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alexander Kuznetsov (Independent Moscow University), Michael Finkelberg","submitted_at":"1999-03-30T18:18:47Z","abstract_excerpt":"We give an example of geometric construction (via Hecke correspondences) of certain representations of the affine Lie algebra $\\hat{gl}_n$. The construction is similar to the one of [FK] for the Lie algebra $sl_n$. Given a surface with a smooth embedded curve $C$ we consider the moduli spaces $K_\\alpha$ of rank $n$ parabolic sheaves satisfying certain conditions. The top dimensional irreducible components of $K_\\alpha$ are numbered by the isomorphism classes of $\\alpha$-dimensional nilpotent representations of the cyclic quiver $\\tilde{A}_{n-1}$. Summing up over all $\\alpha\\in{\\Bbb N}[{\\Bbb Z}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9903181","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"}