{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:6UJKFKNEJEG7EBRP4LO3BJY6XV","short_pith_number":"pith:6UJKFKNE","canonical_record":{"source":{"id":"1701.06114","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-01-22T02:33:01Z","cross_cats_sorted":["math-ph","math.MP","math.RT"],"title_canon_sha256":"aa180ce656ade6001b75a07ff765aa8587978d18ca4f97188af32d42a1ce9002","abstract_canon_sha256":"de866f2b05324f3241696f20bfe0abdb22db8fa96e7b1d3a339f6b70e6a52c48"},"schema_version":"1.0"},"canonical_sha256":"f512a2a9a4490df2062fe2ddb0a71ebd7017b2033b1edf47e6fcc7ed0ba057d1","source":{"kind":"arxiv","id":"1701.06114","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.06114","created_at":"2026-05-18T00:52:19Z"},{"alias_kind":"arxiv_version","alias_value":"1701.06114v1","created_at":"2026-05-18T00:52:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06114","created_at":"2026-05-18T00:52:19Z"},{"alias_kind":"pith_short_12","alias_value":"6UJKFKNEJEG7","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6UJKFKNEJEG7EBRP","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6UJKFKNE","created_at":"2026-05-18T12:31:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:6UJKFKNEJEG7EBRP4LO3BJY6XV","target":"record","payload":{"canonical_record":{"source":{"id":"1701.06114","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-01-22T02:33:01Z","cross_cats_sorted":["math-ph","math.MP","math.RT"],"title_canon_sha256":"aa180ce656ade6001b75a07ff765aa8587978d18ca4f97188af32d42a1ce9002","abstract_canon_sha256":"de866f2b05324f3241696f20bfe0abdb22db8fa96e7b1d3a339f6b70e6a52c48"},"schema_version":"1.0"},"canonical_sha256":"f512a2a9a4490df2062fe2ddb0a71ebd7017b2033b1edf47e6fcc7ed0ba057d1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:19.267061Z","signature_b64":"WVCzE4NARVWtRxTZRqUHjiiPPzkEy0jUJlPQyxkGHGJOwNKL5IjTzu8NV78iZ6rkpwu8nN11CGGWf2n0oBvWAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f512a2a9a4490df2062fe2ddb0a71ebd7017b2033b1edf47e6fcc7ed0ba057d1","last_reissued_at":"2026-05-18T00:52:19.266515Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:19.266515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.06114","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:52:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iiJgWge+4T4fyb4tuRm+sZqp+w7EM3l5FfHUaYQHpDfpAYq3kXXG8uSPIPlWe7PKT3t/oWf7+r1y/3Ri95zJAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T11:28:44.486834Z"},"content_sha256":"9fbdbc9452e21cfc96e4b0d199461aaec1db74806d914e65f19747b705f05130","schema_version":"1.0","event_id":"sha256:9fbdbc9452e21cfc96e4b0d199461aaec1db74806d914e65f19747b705f05130"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:6UJKFKNEJEG7EBRP4LO3BJY6XV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometric Schur Duality of two parameter quantum group of type A","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.RT"],"primary_cat":"math.QA","authors_text":"Haitao Ma, Zhu-Jun Zheng, Zongzhu Lin","submitted_at":"2017-01-22T02:33:01Z","abstract_excerpt":"In this paper, we give an geometric description of the Schur-Weyl duality for two-parameter quantum algebras $U_{v, t}(gl_n)$, where $U_{v, t}(gl_n)$ is the deformation of $U_v(I, \\cdot)$, the classic Shur-Weyl duality $(U_{r, s}(gl_n), V^{\\otimes d}, H_d(r, s))$ can be seen as a corollary of the Shur-Weyl duality $(U_{v, t}(gl_n), V^{\\otimes d}, H_d(v, t))$ by using the galois descend approach. we also establish the Shur-Weyl duality between the algebras $\\widetilde{U_{v, t}(gl_N)^m}$, $\\widehat{U_{v, t}(gl_N)^m}$ and Heck algebra $H_k(v, t)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06114","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:52:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0ZUorn4d58Q3haBpF6QSa09kJirb24klkkjwIfRc4MQ/KORZRwDGk1f3Hcm0RwlAhRmnsuSTTKcUSYEFLiiGBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T11:28:44.487264Z"},"content_sha256":"fe48e2ff4fb63adae2f837da60b967225d51a08f106cf2a5ce11f72ed92ea67d","schema_version":"1.0","event_id":"sha256:fe48e2ff4fb63adae2f837da60b967225d51a08f106cf2a5ce11f72ed92ea67d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6UJKFKNEJEG7EBRP4LO3BJY6XV/bundle.json","state_url":"https://pith.science/pith/6UJKFKNEJEG7EBRP4LO3BJY6XV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6UJKFKNEJEG7EBRP4LO3BJY6XV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T11:28:44Z","links":{"resolver":"https://pith.science/pith/6UJKFKNEJEG7EBRP4LO3BJY6XV","bundle":"https://pith.science/pith/6UJKFKNEJEG7EBRP4LO3BJY6XV/bundle.json","state":"https://pith.science/pith/6UJKFKNEJEG7EBRP4LO3BJY6XV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6UJKFKNEJEG7EBRP4LO3BJY6XV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6UJKFKNEJEG7EBRP4LO3BJY6XV","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"de866f2b05324f3241696f20bfe0abdb22db8fa96e7b1d3a339f6b70e6a52c48","cross_cats_sorted":["math-ph","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-01-22T02:33:01Z","title_canon_sha256":"aa180ce656ade6001b75a07ff765aa8587978d18ca4f97188af32d42a1ce9002"},"schema_version":"1.0","source":{"id":"1701.06114","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.06114","created_at":"2026-05-18T00:52:19Z"},{"alias_kind":"arxiv_version","alias_value":"1701.06114v1","created_at":"2026-05-18T00:52:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06114","created_at":"2026-05-18T00:52:19Z"},{"alias_kind":"pith_short_12","alias_value":"6UJKFKNEJEG7","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6UJKFKNEJEG7EBRP","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6UJKFKNE","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:fe48e2ff4fb63adae2f837da60b967225d51a08f106cf2a5ce11f72ed92ea67d","target":"graph","created_at":"2026-05-18T00:52:19Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we give an geometric description of the Schur-Weyl duality for two-parameter quantum algebras $U_{v, t}(gl_n)$, where $U_{v, t}(gl_n)$ is the deformation of $U_v(I, \\cdot)$, the classic Shur-Weyl duality $(U_{r, s}(gl_n), V^{\\otimes d}, H_d(r, s))$ can be seen as a corollary of the Shur-Weyl duality $(U_{v, t}(gl_n), V^{\\otimes d}, H_d(v, t))$ by using the galois descend approach. we also establish the Shur-Weyl duality between the algebras $\\widetilde{U_{v, t}(gl_N)^m}$, $\\widehat{U_{v, t}(gl_N)^m}$ and Heck algebra $H_k(v, t)$.","authors_text":"Haitao Ma, Zhu-Jun Zheng, Zongzhu Lin","cross_cats":["math-ph","math.MP","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-01-22T02:33:01Z","title":"Geometric Schur Duality of two parameter quantum group of type A"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06114","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:9fbdbc9452e21cfc96e4b0d199461aaec1db74806d914e65f19747b705f05130","target":"record","created_at":"2026-05-18T00:52:19Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"de866f2b05324f3241696f20bfe0abdb22db8fa96e7b1d3a339f6b70e6a52c48","cross_cats_sorted":["math-ph","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-01-22T02:33:01Z","title_canon_sha256":"aa180ce656ade6001b75a07ff765aa8587978d18ca4f97188af32d42a1ce9002"},"schema_version":"1.0","source":{"id":"1701.06114","kind":"arxiv","version":1}},"canonical_sha256":"f512a2a9a4490df2062fe2ddb0a71ebd7017b2033b1edf47e6fcc7ed0ba057d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f512a2a9a4490df2062fe2ddb0a71ebd7017b2033b1edf47e6fcc7ed0ba057d1","first_computed_at":"2026-05-18T00:52:19.266515Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:19.266515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WVCzE4NARVWtRxTZRqUHjiiPPzkEy0jUJlPQyxkGHGJOwNKL5IjTzu8NV78iZ6rkpwu8nN11CGGWf2n0oBvWAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:19.267061Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.06114","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9fbdbc9452e21cfc96e4b0d199461aaec1db74806d914e65f19747b705f05130","sha256:fe48e2ff4fb63adae2f837da60b967225d51a08f106cf2a5ce11f72ed92ea67d"],"state_sha256":"0934013eec79e25fde6c65489ccb2cdff604dbcff35929090f15a2534adfc778"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DkwZ6Nwk1dcLRwj6gJlPGJy6cygwZk9q2Jjg825U30a5ddN1XQvR7r1XzwOi2Lz6hwReyehUPOUU3eJ2wc7tAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T11:28:44.490693Z","bundle_sha256":"f351326c11f426044327292d777f9a43009f600f8cbb656d57f5e100d4f2e824"}}