{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1999:S6FT6IE6D4GORBYV7PCBEUFZNF","short_pith_number":"pith:S6FT6IE6","schema_version":"1.0","canonical_sha256":"978b3f209e1f0ce88715fbc41250b9697ec340e710d924e1791794816f327910","source":{"kind":"arxiv","id":"math/9903181","version":2},"attestation_state":"computed","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}"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/9903181","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"1999-03-30T18:18:47Z","cross_cats_sorted":[],"title_canon_sha256":"1ed91fb83cac05f3bc885eef0e33feb31b94485637a74bc663a87652cb35ad93","abstract_canon_sha256":"d8b825bcc7864487aa4f7efb57a1fc6634f5714f9a9f0b0262e84c5cfa757117"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:33.228091Z","signature_b64":"3fcRkykptWfYzQTc58JbnhhziCj86Y4i998Bnj1Wlr2Omn0U+VTEWbFgidgkSQeCISX+qSygd4aK+OM6Iz+eAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"978b3f209e1f0ce88715fbc41250b9697ec340e710d924e1791794816f327910","last_reissued_at":"2026-05-18T01:05:33.227475Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:33.227475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/9903181","created_at":"2026-05-18T01:05:33.227554+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9903181v2","created_at":"2026-05-18T01:05:33.227554+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9903181","created_at":"2026-05-18T01:05:33.227554+00:00"},{"alias_kind":"pith_short_12","alias_value":"S6FT6IE6D4GO","created_at":"2026-05-18T12:25:49.631198+00:00"},{"alias_kind":"pith_short_16","alias_value":"S6FT6IE6D4GORBYV","created_at":"2026-05-18T12:25:49.631198+00:00"},{"alias_kind":"pith_short_8","alias_value":"S6FT6IE6","created_at":"2026-05-18T12:25:49.631198+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/S6FT6IE6D4GORBYV7PCBEUFZNF","json":"https://pith.science/pith/S6FT6IE6D4GORBYV7PCBEUFZNF.json","graph_json":"https://pith.science/api/pith-number/S6FT6IE6D4GORBYV7PCBEUFZNF/graph.json","events_json":"https://pith.science/api/pith-number/S6FT6IE6D4GORBYV7PCBEUFZNF/events.json","paper":"https://pith.science/paper/S6FT6IE6"},"agent_actions":{"view_html":"https://pith.science/pith/S6FT6IE6D4GORBYV7PCBEUFZNF","download_json":"https://pith.science/pith/S6FT6IE6D4GORBYV7PCBEUFZNF.json","view_paper":"https://pith.science/paper/S6FT6IE6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9903181&json=true","fetch_graph":"https://pith.science/api/pith-number/S6FT6IE6D4GORBYV7PCBEUFZNF/graph.json","fetch_events":"https://pith.science/api/pith-number/S6FT6IE6D4GORBYV7PCBEUFZNF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S6FT6IE6D4GORBYV7PCBEUFZNF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S6FT6IE6D4GORBYV7PCBEUFZNF/action/storage_attestation","attest_author":"https://pith.science/pith/S6FT6IE6D4GORBYV7PCBEUFZNF/action/author_attestation","sign_citation":"https://pith.science/pith/S6FT6IE6D4GORBYV7PCBEUFZNF/action/citation_signature","submit_replication":"https://pith.science/pith/S6FT6IE6D4GORBYV7PCBEUFZNF/action/replication_record"}},"created_at":"2026-05-18T01:05:33.227554+00:00","updated_at":"2026-05-18T01:05:33.227554+00:00"}