{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:YZNZVTGUCD6DTOHLQYWZU7SLU4","short_pith_number":"pith:YZNZVTGU","schema_version":"1.0","canonical_sha256":"c65b9accd410fc39b8eb862d9a7e4ba727457a74528b24a30638581eef09ceec","source":{"kind":"arxiv","id":"2403.15968","version":3},"attestation_state":"computed","paper":{"title":"Symplectic Differential Reduction Algebras and Generalized Weyl Algebras","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.QA","math.RA"],"primary_cat":"math.RT","authors_text":"Dwight Anderson Williams II, Jonas T. Hartwig","submitted_at":"2024-03-24T00:08:32Z","abstract_excerpt":"Given a map $\\Xi\\colon U(\\mathfrak{g})\\rightarrow A$ of associative algebras, with $U(\\mathfrak{g})$ the universal enveloping algebra of a (complex) finite-dimensional reductive Lie algebra $\\mathfrak{g}$, the restriction functor from $A$-modules to $U(\\mathfrak{g})$-modules is intimately tied to the representation theory of an $A$-subquotient known as the reduction algebra with respect to $(A,\\mathfrak{g},\\Xi)$. Herlemont and Ogievetsky described differential reduction algebras for the general linear Lie algebra $\\mathfrak{gl}(n)$ as algebras of deformed differential operators. Their map $\\Xi"},"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":"2403.15968","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.RT","submitted_at":"2024-03-24T00:08:32Z","cross_cats_sorted":["math.QA","math.RA"],"title_canon_sha256":"ea213d4fd4ffa579270844f29a801c1b4d2b9c46de2f2ffaf957ccd304186764","abstract_canon_sha256":"0119f9300d60081fe7e420efc006d83c00e5a48613eebd1fd44327d5456a1e9a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:55:55.979842Z","signature_b64":"p9jzH746MwBkTTYr54ClnNqn+denqx8Sr0I3/j94uTHgoHGC5yxpJYGl4VZ7F8WDEpoHc8fRzL1Q9A963Bs0Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c65b9accd410fc39b8eb862d9a7e4ba727457a74528b24a30638581eef09ceec","last_reissued_at":"2026-07-05T09:55:55.979393Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:55:55.979393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Symplectic Differential Reduction Algebras and Generalized Weyl Algebras","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.QA","math.RA"],"primary_cat":"math.RT","authors_text":"Dwight Anderson Williams II, Jonas T. Hartwig","submitted_at":"2024-03-24T00:08:32Z","abstract_excerpt":"Given a map $\\Xi\\colon U(\\mathfrak{g})\\rightarrow A$ of associative algebras, with $U(\\mathfrak{g})$ the universal enveloping algebra of a (complex) finite-dimensional reductive Lie algebra $\\mathfrak{g}$, the restriction functor from $A$-modules to $U(\\mathfrak{g})$-modules is intimately tied to the representation theory of an $A$-subquotient known as the reduction algebra with respect to $(A,\\mathfrak{g},\\Xi)$. Herlemont and Ogievetsky described differential reduction algebras for the general linear Lie algebra $\\mathfrak{gl}(n)$ as algebras of deformed differential operators. Their map $\\Xi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.15968","kind":"arxiv","version":3},"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/2403.15968/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":"2403.15968","created_at":"2026-07-05T09:55:55.979450+00:00"},{"alias_kind":"arxiv_version","alias_value":"2403.15968v3","created_at":"2026-07-05T09:55:55.979450+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.15968","created_at":"2026-07-05T09:55:55.979450+00:00"},{"alias_kind":"pith_short_12","alias_value":"YZNZVTGUCD6D","created_at":"2026-07-05T09:55:55.979450+00:00"},{"alias_kind":"pith_short_16","alias_value":"YZNZVTGUCD6DTOHL","created_at":"2026-07-05T09:55:55.979450+00:00"},{"alias_kind":"pith_short_8","alias_value":"YZNZVTGU","created_at":"2026-07-05T09:55:55.979450+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/YZNZVTGUCD6DTOHLQYWZU7SLU4","json":"https://pith.science/pith/YZNZVTGUCD6DTOHLQYWZU7SLU4.json","graph_json":"https://pith.science/api/pith-number/YZNZVTGUCD6DTOHLQYWZU7SLU4/graph.json","events_json":"https://pith.science/api/pith-number/YZNZVTGUCD6DTOHLQYWZU7SLU4/events.json","paper":"https://pith.science/paper/YZNZVTGU"},"agent_actions":{"view_html":"https://pith.science/pith/YZNZVTGUCD6DTOHLQYWZU7SLU4","download_json":"https://pith.science/pith/YZNZVTGUCD6DTOHLQYWZU7SLU4.json","view_paper":"https://pith.science/paper/YZNZVTGU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2403.15968&json=true","fetch_graph":"https://pith.science/api/pith-number/YZNZVTGUCD6DTOHLQYWZU7SLU4/graph.json","fetch_events":"https://pith.science/api/pith-number/YZNZVTGUCD6DTOHLQYWZU7SLU4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YZNZVTGUCD6DTOHLQYWZU7SLU4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YZNZVTGUCD6DTOHLQYWZU7SLU4/action/storage_attestation","attest_author":"https://pith.science/pith/YZNZVTGUCD6DTOHLQYWZU7SLU4/action/author_attestation","sign_citation":"https://pith.science/pith/YZNZVTGUCD6DTOHLQYWZU7SLU4/action/citation_signature","submit_replication":"https://pith.science/pith/YZNZVTGUCD6DTOHLQYWZU7SLU4/action/replication_record"}},"created_at":"2026-07-05T09:55:55.979450+00:00","updated_at":"2026-07-05T09:55:55.979450+00:00"}