{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:D3VOJ3EVBWAOQS3BFWNMQJSRK3","short_pith_number":"pith:D3VOJ3EV","schema_version":"1.0","canonical_sha256":"1eeae4ec950d80e84b612d9ac8265156f4f39da16767c336115a106a5d87f8d4","source":{"kind":"arxiv","id":"1905.01828","version":1},"attestation_state":"computed","paper":{"title":"The regular representation of $U_v(\\mathfrak{gl}_{m|n})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA","math.RT"],"primary_cat":"math.QA","authors_text":"Jie Du, Zhongguo Zhou","submitted_at":"2019-05-06T06:00:21Z","abstract_excerpt":"Using quantum differential operators, we construct a super representation of $U_v(\\mathfrak{gl}_{m|n})$ on a certain polynomial superalgebra. We then extend the representation to its formal power series algebra which contains a $U_v(\\mathfrak{gl}_{m|n})$-submodule isomorphic to the regular representation of $U_v(\\mathfrak{gl}_{m|n})$. In this way, we obtain a presentation of $U_v(\\mathfrak{gl}_{m|n})$ by a basis together with explicit multiplication formulas of the basis elements by generators."},"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":"1905.01828","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2019-05-06T06:00:21Z","cross_cats_sorted":["math.RA","math.RT"],"title_canon_sha256":"cc7354d97c78928d536c0485003ab8043bbb1ce72e5571ae33276436193c1530","abstract_canon_sha256":"d9f48a3a89ebd4e0c29ecb0bd992a330fdcb4d48f528834ae7dc318bc2a5978a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:57.297276Z","signature_b64":"O3xuHeN1eetkYJMwEGMNhoPnhUmPbkcr5+/e/02sLGlSgGskKS4A/7Luy1Qq89ivH7MipihOiH7aQDnUnMelCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1eeae4ec950d80e84b612d9ac8265156f4f39da16767c336115a106a5d87f8d4","last_reissued_at":"2026-05-17T23:46:57.296644Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:57.296644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The regular representation of $U_v(\\mathfrak{gl}_{m|n})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA","math.RT"],"primary_cat":"math.QA","authors_text":"Jie Du, Zhongguo Zhou","submitted_at":"2019-05-06T06:00:21Z","abstract_excerpt":"Using quantum differential operators, we construct a super representation of $U_v(\\mathfrak{gl}_{m|n})$ on a certain polynomial superalgebra. We then extend the representation to its formal power series algebra which contains a $U_v(\\mathfrak{gl}_{m|n})$-submodule isomorphic to the regular representation of $U_v(\\mathfrak{gl}_{m|n})$. In this way, we obtain a presentation of $U_v(\\mathfrak{gl}_{m|n})$ by a basis together with explicit multiplication formulas of the basis elements by generators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.01828","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1905.01828","created_at":"2026-05-17T23:46:57.296732+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.01828v1","created_at":"2026-05-17T23:46:57.296732+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.01828","created_at":"2026-05-17T23:46:57.296732+00:00"},{"alias_kind":"pith_short_12","alias_value":"D3VOJ3EVBWAO","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_16","alias_value":"D3VOJ3EVBWAOQS3B","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_8","alias_value":"D3VOJ3EV","created_at":"2026-05-18T12:33:15.570797+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/D3VOJ3EVBWAOQS3BFWNMQJSRK3","json":"https://pith.science/pith/D3VOJ3EVBWAOQS3BFWNMQJSRK3.json","graph_json":"https://pith.science/api/pith-number/D3VOJ3EVBWAOQS3BFWNMQJSRK3/graph.json","events_json":"https://pith.science/api/pith-number/D3VOJ3EVBWAOQS3BFWNMQJSRK3/events.json","paper":"https://pith.science/paper/D3VOJ3EV"},"agent_actions":{"view_html":"https://pith.science/pith/D3VOJ3EVBWAOQS3BFWNMQJSRK3","download_json":"https://pith.science/pith/D3VOJ3EVBWAOQS3BFWNMQJSRK3.json","view_paper":"https://pith.science/paper/D3VOJ3EV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.01828&json=true","fetch_graph":"https://pith.science/api/pith-number/D3VOJ3EVBWAOQS3BFWNMQJSRK3/graph.json","fetch_events":"https://pith.science/api/pith-number/D3VOJ3EVBWAOQS3BFWNMQJSRK3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/D3VOJ3EVBWAOQS3BFWNMQJSRK3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/D3VOJ3EVBWAOQS3BFWNMQJSRK3/action/storage_attestation","attest_author":"https://pith.science/pith/D3VOJ3EVBWAOQS3BFWNMQJSRK3/action/author_attestation","sign_citation":"https://pith.science/pith/D3VOJ3EVBWAOQS3BFWNMQJSRK3/action/citation_signature","submit_replication":"https://pith.science/pith/D3VOJ3EVBWAOQS3BFWNMQJSRK3/action/replication_record"}},"created_at":"2026-05-17T23:46:57.296732+00:00","updated_at":"2026-05-17T23:46:57.296732+00:00"}