{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:TNRYP34HJ3FCCWC7HJ2J5OFZBE","short_pith_number":"pith:TNRYP34H","schema_version":"1.0","canonical_sha256":"9b6387ef874eca21585f3a749eb8b9090b08a802320d296bd03ab7ccefeb8852","source":{"kind":"arxiv","id":"1811.01011","version":2},"attestation_state":"computed","paper":{"title":"Affine Laumon spaces and a conjecture of Kuznetsov","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Andrei Negu\\c{t}","submitted_at":"2018-11-02T17:52:18Z","abstract_excerpt":"We prove a conjecture of Kuznetsov stating that the equivariant K-theory of affine Laumon spaces is the universal Verma module for the quantum affine algebra U_q(gl_n^). We do so by reinterpreting the action of the quantum toroidal algebra U_q(gl_n^^) on the K-theory from [14] in terms of the shuffle algebra studied in [12], which constructs an embedding of U_q(gl_n^) into U_q(gl_n^^)"},"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":"1811.01011","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-11-02T17:52:18Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"fcf3746859d9f8cddf8f0a0908bf0e2f70b93ef69c8c047ba3632a71f1d5f653","abstract_canon_sha256":"27432c23d8a7e3be447886aa4684d61affc0d429d8c0996d47d15d725150b1a2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:28:58.395796Z","signature_b64":"n2Mng0q92mO/dm4xb1/IM4muMwMS1Nr2Wwx/JntDaIggC8nGdTD8VGoWpO0UDVXXWaJGq6Dhgu+z2UwD9tmEDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b6387ef874eca21585f3a749eb8b9090b08a802320d296bd03ab7ccefeb8852","last_reissued_at":"2026-07-05T01:28:58.395392Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:28:58.395392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Affine Laumon spaces and a conjecture of Kuznetsov","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Andrei Negu\\c{t}","submitted_at":"2018-11-02T17:52:18Z","abstract_excerpt":"We prove a conjecture of Kuznetsov stating that the equivariant K-theory of affine Laumon spaces is the universal Verma module for the quantum affine algebra U_q(gl_n^). We do so by reinterpreting the action of the quantum toroidal algebra U_q(gl_n^^) on the K-theory from [14] in terms of the shuffle algebra studied in [12], which constructs an embedding of U_q(gl_n^) into U_q(gl_n^^)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.01011","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1811.01011/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1811.01011","created_at":"2026-07-05T01:28:58.395450+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.01011v2","created_at":"2026-07-05T01:28:58.395450+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.01011","created_at":"2026-07-05T01:28:58.395450+00:00"},{"alias_kind":"pith_short_12","alias_value":"TNRYP34HJ3FC","created_at":"2026-07-05T01:28:58.395450+00:00"},{"alias_kind":"pith_short_16","alias_value":"TNRYP34HJ3FCCWC7","created_at":"2026-07-05T01:28:58.395450+00:00"},{"alias_kind":"pith_short_8","alias_value":"TNRYP34H","created_at":"2026-07-05T01:28:58.395450+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2412.00912","citing_title":"Classical elliptic integrable systems from the moduli space of instantons","ref_index":35,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TNRYP34HJ3FCCWC7HJ2J5OFZBE","json":"https://pith.science/pith/TNRYP34HJ3FCCWC7HJ2J5OFZBE.json","graph_json":"https://pith.science/api/pith-number/TNRYP34HJ3FCCWC7HJ2J5OFZBE/graph.json","events_json":"https://pith.science/api/pith-number/TNRYP34HJ3FCCWC7HJ2J5OFZBE/events.json","paper":"https://pith.science/paper/TNRYP34H"},"agent_actions":{"view_html":"https://pith.science/pith/TNRYP34HJ3FCCWC7HJ2J5OFZBE","download_json":"https://pith.science/pith/TNRYP34HJ3FCCWC7HJ2J5OFZBE.json","view_paper":"https://pith.science/paper/TNRYP34H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.01011&json=true","fetch_graph":"https://pith.science/api/pith-number/TNRYP34HJ3FCCWC7HJ2J5OFZBE/graph.json","fetch_events":"https://pith.science/api/pith-number/TNRYP34HJ3FCCWC7HJ2J5OFZBE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TNRYP34HJ3FCCWC7HJ2J5OFZBE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TNRYP34HJ3FCCWC7HJ2J5OFZBE/action/storage_attestation","attest_author":"https://pith.science/pith/TNRYP34HJ3FCCWC7HJ2J5OFZBE/action/author_attestation","sign_citation":"https://pith.science/pith/TNRYP34HJ3FCCWC7HJ2J5OFZBE/action/citation_signature","submit_replication":"https://pith.science/pith/TNRYP34HJ3FCCWC7HJ2J5OFZBE/action/replication_record"}},"created_at":"2026-07-05T01:28:58.395450+00:00","updated_at":"2026-07-05T01:28:58.395450+00:00"}