{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1998:CLLJBPZO7WH4AYR44LTWZATSCJ","short_pith_number":"pith:CLLJBPZO","schema_version":"1.0","canonical_sha256":"12d690bf2efd8fc0623ce2e76c8272124ec32725afcd4a81e164d6f41f03088c","source":{"kind":"arxiv","id":"math/9808023","version":1},"attestation_state":"computed","paper":{"title":"Toroidal and level 0 U'_q(\\hat{sl_{n+1}}) actions on U_q(\\hat{gl_{n+1}}) modules","license":"","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Kei Miki","submitted_at":"1998-08-05T10:52:23Z","abstract_excerpt":"(1) Utilizing a Braid group action on a completion of U_q(\\hat{sl_{n+1}}), an algebra homomorphism from the toroidal algebra U_q(sl_{n+1,tor}) (n\\ge 2) with fixed parameter to a completion of U_q(\\hat{gl_{n+1}}) is obtained.\n  (2) The toroidal actions by Saito induces a level 0 U'_q(\\hat{sl_{n+1}}) action on level 1 integrable highest weight modules of U_q(\\hat{sl_{n+1}}). Another level 0 U'_q(\\hat{sl_{n+1}}) action is defined by Jimbo, et al., in the case n=1. Using the fact that the intertwiners of U_q(\\hat{sl_{n+1}}) modules are intertwiners of toroidal modules for an appropriate comultipli"},"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/9808023","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"1998-08-05T10:52:23Z","cross_cats_sorted":[],"title_canon_sha256":"f3ca02ebd4769a88539f9917df1cde1b4bb526ac5a4c1a989302069a191d2a05","abstract_canon_sha256":"8fb5d006eb897404b4b5afb654e7458d8d4e780c6d30d2c57fcbb283b815c119"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:22.803603Z","signature_b64":"WBTFjnW3lnqv+so2naQNOs77dbv2YNYwS1w+qlGeFR13lAcMPC9cXJbw+au1IwDgFybyRqqUTAMajMJ8Lh18Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12d690bf2efd8fc0623ce2e76c8272124ec32725afcd4a81e164d6f41f03088c","last_reissued_at":"2026-05-18T01:38:22.802920Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:22.802920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Toroidal and level 0 U'_q(\\hat{sl_{n+1}}) actions on U_q(\\hat{gl_{n+1}}) modules","license":"","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Kei Miki","submitted_at":"1998-08-05T10:52:23Z","abstract_excerpt":"(1) Utilizing a Braid group action on a completion of U_q(\\hat{sl_{n+1}}), an algebra homomorphism from the toroidal algebra U_q(sl_{n+1,tor}) (n\\ge 2) with fixed parameter to a completion of U_q(\\hat{gl_{n+1}}) is obtained.\n  (2) The toroidal actions by Saito induces a level 0 U'_q(\\hat{sl_{n+1}}) action on level 1 integrable highest weight modules of U_q(\\hat{sl_{n+1}}). Another level 0 U'_q(\\hat{sl_{n+1}}) action is defined by Jimbo, et al., in the case n=1. Using the fact that the intertwiners of U_q(\\hat{sl_{n+1}}) modules are intertwiners of toroidal modules for an appropriate comultipli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9808023","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":"math/9808023","created_at":"2026-05-18T01:38:22.803022+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9808023v1","created_at":"2026-05-18T01:38:22.803022+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9808023","created_at":"2026-05-18T01:38:22.803022+00:00"},{"alias_kind":"pith_short_12","alias_value":"CLLJBPZO7WH4","created_at":"2026-05-18T12:25:49.038998+00:00"},{"alias_kind":"pith_short_16","alias_value":"CLLJBPZO7WH4AYR4","created_at":"2026-05-18T12:25:49.038998+00:00"},{"alias_kind":"pith_short_8","alias_value":"CLLJBPZO","created_at":"2026-05-18T12:25:49.038998+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/CLLJBPZO7WH4AYR44LTWZATSCJ","json":"https://pith.science/pith/CLLJBPZO7WH4AYR44LTWZATSCJ.json","graph_json":"https://pith.science/api/pith-number/CLLJBPZO7WH4AYR44LTWZATSCJ/graph.json","events_json":"https://pith.science/api/pith-number/CLLJBPZO7WH4AYR44LTWZATSCJ/events.json","paper":"https://pith.science/paper/CLLJBPZO"},"agent_actions":{"view_html":"https://pith.science/pith/CLLJBPZO7WH4AYR44LTWZATSCJ","download_json":"https://pith.science/pith/CLLJBPZO7WH4AYR44LTWZATSCJ.json","view_paper":"https://pith.science/paper/CLLJBPZO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9808023&json=true","fetch_graph":"https://pith.science/api/pith-number/CLLJBPZO7WH4AYR44LTWZATSCJ/graph.json","fetch_events":"https://pith.science/api/pith-number/CLLJBPZO7WH4AYR44LTWZATSCJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CLLJBPZO7WH4AYR44LTWZATSCJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CLLJBPZO7WH4AYR44LTWZATSCJ/action/storage_attestation","attest_author":"https://pith.science/pith/CLLJBPZO7WH4AYR44LTWZATSCJ/action/author_attestation","sign_citation":"https://pith.science/pith/CLLJBPZO7WH4AYR44LTWZATSCJ/action/citation_signature","submit_replication":"https://pith.science/pith/CLLJBPZO7WH4AYR44LTWZATSCJ/action/replication_record"}},"created_at":"2026-05-18T01:38:22.803022+00:00","updated_at":"2026-05-18T01:38:22.803022+00:00"}