{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:IJQFXPIUIGHWCR7QIDA7ZWV4XF","short_pith_number":"pith:IJQFXPIU","schema_version":"1.0","canonical_sha256":"42605bbd14418f6147f040c1fcdabcb951b41eda6f48a86723e750dc72d4c280","source":{"kind":"arxiv","id":"2406.02870","version":3},"attestation_state":"computed","paper":{"title":"Unipotent quantum coordinate ring and cominuscule prefundamental representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Euiyong Park, Il-Seung Jang, Jae-Hoon Kwon","submitted_at":"2024-06-05T02:32:27Z","abstract_excerpt":"We continue the study of realization of the prefundamental modules $L_{r,a}^{\\pm}$, introduced by Hernandez and Jimbo, in terms of unipotent quantum coordinate rings as in [J-Kwon-Park, Int. Math. Res. Not., 2023]. We show that the ordinary character of $L_{r,a}^{\\pm}$ is equal to that of the unipotent quantum coordinate ring $U_q^-(w_r)$ associated to fundamental $r$-th coweight. When $r$ is cominuscule, we prove that there exists a $U_q(\\mathfrak{b})$-module structure on $U_q^-(w_r)$, which is isomorphic to $L_{r,a\\eta_r}^\\pm$ for some $\\eta_r \\in \\mathbb{C}^\\times$."},"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":"2406.02870","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-06-05T02:32:27Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"a78035849a1a27ed7f344a3c411140c27a4a06ec82a309ead03d4acc7c2b92ee","abstract_canon_sha256":"fd42e25d9bb0ee1184cdcd0bcd6aad0466021b0efd7d74ac6eb55390c6c0f895"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"42605bbd14418f6147f040c1fcdabcb951b41eda6f48a86723e750dc72d4c280","last_reissued_at":"2026-07-30T01:15:49.235024Z","signature_status":"unsigned_v0","first_computed_at":"2026-07-30T01:15:49.235024Z"},"graph_snapshot":{"paper":{"title":"Unipotent quantum coordinate ring and cominuscule prefundamental representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Euiyong Park, Il-Seung Jang, Jae-Hoon Kwon","submitted_at":"2024-06-05T02:32:27Z","abstract_excerpt":"We continue the study of realization of the prefundamental modules $L_{r,a}^{\\pm}$, introduced by Hernandez and Jimbo, in terms of unipotent quantum coordinate rings as in [J-Kwon-Park, Int. Math. Res. Not., 2023]. We show that the ordinary character of $L_{r,a}^{\\pm}$ is equal to that of the unipotent quantum coordinate ring $U_q^-(w_r)$ associated to fundamental $r$-th coweight. When $r$ is cominuscule, we prove that there exists a $U_q(\\mathfrak{b})$-module structure on $U_q^-(w_r)$, which is isomorphic to $L_{r,a\\eta_r}^\\pm$ for some $\\eta_r \\in \\mathbb{C}^\\times$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.02870","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/2406.02870/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":"2406.02870","created_at":"2026-07-30T01:15:49.241305+00:00"},{"alias_kind":"arxiv_version","alias_value":"2406.02870v3","created_at":"2026-07-30T01:15:49.241305+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.02870","created_at":"2026-07-30T01:15:49.241305+00:00"},{"alias_kind":"pith_short_12","alias_value":"IJQFXPIUIGHW","created_at":"2026-07-30T01:15:49.241305+00:00"},{"alias_kind":"pith_short_16","alias_value":"IJQFXPIUIGHWCR7Q","created_at":"2026-07-30T01:15:49.241305+00:00"},{"alias_kind":"pith_short_8","alias_value":"IJQFXPIU","created_at":"2026-07-30T01:15:49.241305+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2509.01412","citing_title":"Vis-CoT: A Human-in-the-Loop Framework for Interactive Visualization and Intervention in LLM Chain-of-Thought Reasoning","ref_index":39,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IJQFXPIUIGHWCR7QIDA7ZWV4XF","json":"https://pith.science/pith/IJQFXPIUIGHWCR7QIDA7ZWV4XF.json","graph_json":"https://pith.science/api/pith-number/IJQFXPIUIGHWCR7QIDA7ZWV4XF/graph.json","events_json":"https://pith.science/api/pith-number/IJQFXPIUIGHWCR7QIDA7ZWV4XF/events.json","paper":"https://pith.science/paper/IJQFXPIU"},"agent_actions":{"view_html":"https://pith.science/pith/IJQFXPIUIGHWCR7QIDA7ZWV4XF","download_json":"https://pith.science/pith/IJQFXPIUIGHWCR7QIDA7ZWV4XF.json","view_paper":"https://pith.science/paper/IJQFXPIU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2406.02870&json=true","fetch_graph":"https://pith.science/api/pith-number/IJQFXPIUIGHWCR7QIDA7ZWV4XF/graph.json","fetch_events":"https://pith.science/api/pith-number/IJQFXPIUIGHWCR7QIDA7ZWV4XF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IJQFXPIUIGHWCR7QIDA7ZWV4XF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IJQFXPIUIGHWCR7QIDA7ZWV4XF/action/storage_attestation","attest_author":"https://pith.science/pith/IJQFXPIUIGHWCR7QIDA7ZWV4XF/action/author_attestation","sign_citation":"https://pith.science/pith/IJQFXPIUIGHWCR7QIDA7ZWV4XF/action/citation_signature","submit_replication":"https://pith.science/pith/IJQFXPIUIGHWCR7QIDA7ZWV4XF/action/replication_record"}},"created_at":"2026-07-30T01:15:49.241305+00:00","updated_at":"2026-07-30T01:15:49.241305+00:00"}