{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:LZLBYD6YTN7YZPZD5DUAQSDZJQ","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":"d24b37c7a74801ae088fc78ed21d35ec650047b05a43fb661ab865688a651372","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2008-10-07T15:55:47Z","title_canon_sha256":"214d2b1f4fa779061dd9b9b4c54e0e6ce5c077eb704f254d8c5f85c098881de0"},"schema_version":"1.0","source":{"id":"0810.1227","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.1227","created_at":"2026-05-18T03:50:59Z"},{"alias_kind":"arxiv_version","alias_value":"0810.1227v4","created_at":"2026-05-18T03:50:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.1227","created_at":"2026-05-18T03:50:59Z"},{"alias_kind":"pith_short_12","alias_value":"LZLBYD6YTN7Y","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"LZLBYD6YTN7YZPZD","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"LZLBYD6Y","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:a277fc29ea967c3f32551114d7bc12ea020e179751a6fbedb758984b7042c89e","target":"graph","created_at":"2026-05-18T03:50:59Z","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":"Let $R$ be a commutative ring with one and $q$ an invertible element of $R$. The (specialized) quantum group ${\\mathbf U} = U_q(\\mathfrak{gl}_n)$ over $R$ of the general linear group acts on mixed tensor space $V^{\\otimes r}\\otimes {V^*}^{\\otimes s}$ where $V$ denotes the natural $\\mathbf U$-module $R^n$, $r,s$ are nonnegative integers and $V^*$ is the dual $\\mathbf U$-module to $V$. The image of $\\mathbf U$ in $\\mathrm{End}_R(V^{\\otimes r}\\otimes {V^*}^{\\otimes s})$ is called the rational $q$-Schur algebra $S_{q}(n;r,s)$. We construct a bideterminant basis of $S_{q}(n;r,s)$. There is an actio","authors_text":"F. Stoll, R. Dipper, S. Doty","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2008-10-07T15:55:47Z","title":"Quantized mixed tensor space and Schur-Weyl duality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.1227","kind":"arxiv","version":4},"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":"sha256:76b577a035fc80d9569e439dd022b92f53d5d75686074a2fe39ecaecf57cfd6c","target":"record","created_at":"2026-05-18T03:50:59Z","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":"d24b37c7a74801ae088fc78ed21d35ec650047b05a43fb661ab865688a651372","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2008-10-07T15:55:47Z","title_canon_sha256":"214d2b1f4fa779061dd9b9b4c54e0e6ce5c077eb704f254d8c5f85c098881de0"},"schema_version":"1.0","source":{"id":"0810.1227","kind":"arxiv","version":4}},"canonical_sha256":"5e561c0fd89b7f8cbf23e8e80848794c220279cc851636366f81fe03ed37c2f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e561c0fd89b7f8cbf23e8e80848794c220279cc851636366f81fe03ed37c2f5","first_computed_at":"2026-05-18T03:50:59.462990Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:59.462990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Rtow27PmQsUfZ9U28ADRoO1OaNeLthVmxTWtkkHdMqw/V4xarYrN83FeXT+fQz12hlH6EmV/TkXDud0C/tF7Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:59.463702Z","signed_message":"canonical_sha256_bytes"},"source_id":"0810.1227","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:76b577a035fc80d9569e439dd022b92f53d5d75686074a2fe39ecaecf57cfd6c","sha256:a277fc29ea967c3f32551114d7bc12ea020e179751a6fbedb758984b7042c89e"],"state_sha256":"bab5e4058d396b393c3b4953ab3ee3d0a66ef0e5fe6596686c701187b4fdfbff"}