{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:WYTYPO6YWYRB4RFVFW66D6VO7K","short_pith_number":"pith:WYTYPO6Y","schema_version":"1.0","canonical_sha256":"b62787bbd8b6221e44b52dbde1faaefa8e89e0d0540402003ae99374801c9472","source":{"kind":"arxiv","id":"1411.0478","version":2},"attestation_state":"computed","paper":{"title":"Trigonometric weight functions as K-theoretic stable envelope maps for the cotangent bundle of a flag variety","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.AG","authors_text":"A. Varchenko, R. Rimanyi, V. Tarasov","submitted_at":"2014-11-03T13:18:45Z","abstract_excerpt":"We consider the cotangent bundle $T^*F_\\lambda$ of a $GL_n$ partial flag variety, $\\lambda=(\\lambda_1,...,\\lambda_N)$, $|\\lambda|=\\sum_i\\lambda_i=n$, and the torus $T=(\\C^\\times)^{n+1}$ equivariant K-theory algebra $K_T(T^*F_\\lambda)$. We introduce K-theoretic stable envelope maps $\\Stab_{\\sigma}: \\oplus_{|\\lambda|=n} K_T((T^*F_\\lambda)^T)\\to\\oplus_{|\\lambda|=n}K_T(T^*F_\\lambda)$, where $\\sigma\\in S_n$. Using these maps we define a quantum loop algebra action on $\\oplus_{|\\lambda|=n}K_T(T^*F_\\lambda)$. We describe the associated Bethe algebra $B^q(K_T(T^*F_\\lambda))$ by generators and relation"},"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":"1411.0478","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-11-03T13:18:45Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"7072f51ae2e7b13a7d7de6605e0584621ae87dcc12d02f0e154358d915c15914","abstract_canon_sha256":"c3b443692f0ef336377ac83a4f78459e0babd05697146be823ef389a30ac260a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:04:02.653264Z","signature_b64":"OVz2CycJKzXF4tSOXxzTqZgKUSoYC9XE2hPy82681iXIrwZxpCPQikypoJ+2ux78dA+o9tp0N39aoG3t/NeWAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b62787bbd8b6221e44b52dbde1faaefa8e89e0d0540402003ae99374801c9472","last_reissued_at":"2026-05-18T02:04:02.652477Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:04:02.652477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Trigonometric weight functions as K-theoretic stable envelope maps for the cotangent bundle of a flag variety","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.AG","authors_text":"A. Varchenko, R. Rimanyi, V. Tarasov","submitted_at":"2014-11-03T13:18:45Z","abstract_excerpt":"We consider the cotangent bundle $T^*F_\\lambda$ of a $GL_n$ partial flag variety, $\\lambda=(\\lambda_1,...,\\lambda_N)$, $|\\lambda|=\\sum_i\\lambda_i=n$, and the torus $T=(\\C^\\times)^{n+1}$ equivariant K-theory algebra $K_T(T^*F_\\lambda)$. We introduce K-theoretic stable envelope maps $\\Stab_{\\sigma}: \\oplus_{|\\lambda|=n} K_T((T^*F_\\lambda)^T)\\to\\oplus_{|\\lambda|=n}K_T(T^*F_\\lambda)$, where $\\sigma\\in S_n$. Using these maps we define a quantum loop algebra action on $\\oplus_{|\\lambda|=n}K_T(T^*F_\\lambda)$. We describe the associated Bethe algebra $B^q(K_T(T^*F_\\lambda))$ by generators and relation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0478","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":""},"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":"1411.0478","created_at":"2026-05-18T02:04:02.652617+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.0478v2","created_at":"2026-05-18T02:04:02.652617+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.0478","created_at":"2026-05-18T02:04:02.652617+00:00"},{"alias_kind":"pith_short_12","alias_value":"WYTYPO6YWYRB","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_16","alias_value":"WYTYPO6YWYRB4RFV","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_8","alias_value":"WYTYPO6Y","created_at":"2026-05-18T12:28:54.890064+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/WYTYPO6YWYRB4RFVFW66D6VO7K","json":"https://pith.science/pith/WYTYPO6YWYRB4RFVFW66D6VO7K.json","graph_json":"https://pith.science/api/pith-number/WYTYPO6YWYRB4RFVFW66D6VO7K/graph.json","events_json":"https://pith.science/api/pith-number/WYTYPO6YWYRB4RFVFW66D6VO7K/events.json","paper":"https://pith.science/paper/WYTYPO6Y"},"agent_actions":{"view_html":"https://pith.science/pith/WYTYPO6YWYRB4RFVFW66D6VO7K","download_json":"https://pith.science/pith/WYTYPO6YWYRB4RFVFW66D6VO7K.json","view_paper":"https://pith.science/paper/WYTYPO6Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.0478&json=true","fetch_graph":"https://pith.science/api/pith-number/WYTYPO6YWYRB4RFVFW66D6VO7K/graph.json","fetch_events":"https://pith.science/api/pith-number/WYTYPO6YWYRB4RFVFW66D6VO7K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WYTYPO6YWYRB4RFVFW66D6VO7K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WYTYPO6YWYRB4RFVFW66D6VO7K/action/storage_attestation","attest_author":"https://pith.science/pith/WYTYPO6YWYRB4RFVFW66D6VO7K/action/author_attestation","sign_citation":"https://pith.science/pith/WYTYPO6YWYRB4RFVFW66D6VO7K/action/citation_signature","submit_replication":"https://pith.science/pith/WYTYPO6YWYRB4RFVFW66D6VO7K/action/replication_record"}},"created_at":"2026-05-18T02:04:02.652617+00:00","updated_at":"2026-05-18T02:04:02.652617+00:00"}