{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:PCIXJEDO4KNACBGBFGQMKWJKBA","short_pith_number":"pith:PCIXJEDO","schema_version":"1.0","canonical_sha256":"789174906ee29a0104c129a0c5592a081aa7834c52d07e54cb4e8ea43a4a12fe","source":{"kind":"arxiv","id":"1710.10375","version":3},"attestation_state":"computed","paper":{"title":"The $q$-Schur algebras and $q$-Schur dualities of finite type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Li Luo, Weiqiang Wang","submitted_at":"2017-10-28T02:48:45Z","abstract_excerpt":"We formulate a $q$-Schur algebra associated to an arbitrary $W$-invariant finite set $X_{\\texttt f}$ of integral weights for a complex simple Lie algebra with Weyl group $W$. We establish a $q$-Schur duality between the $q$-Schur algebra and Hecke algebra associated to $W$. We then realize geometrically the $q$-Schur algebra and duality, and construct a canonical basis for the $q$-Schur algebra with positivity. With suitable choices of $X_{\\texttt f}$ in classical types, we recover the $q$-Schur algebras in the literature. Our $q$-Schur algebras are closely related to the category $\\mathcal O$"},"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":"1710.10375","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-10-28T02:48:45Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"45d47e711c7e17b06d07d45f2e9f4512fc962576ba80b7af46f1a4dffdb3f1d5","abstract_canon_sha256":"d52d249106ff903bd75fcae76d9e0e0e6f985b52f254d7266fe8d2fb552cb6de"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:57:22.494150Z","signature_b64":"wuUJwwBTvprQu1BysKK20z+lqUBdSERZe9aTKv9oNKGNYHZftZDpSilkglO4qGl6PFYSU7qm7Fmv53gh9CdPAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"789174906ee29a0104c129a0c5592a081aa7834c52d07e54cb4e8ea43a4a12fe","last_reissued_at":"2026-07-05T03:57:22.493673Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:57:22.493673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The $q$-Schur algebras and $q$-Schur dualities of finite type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Li Luo, Weiqiang Wang","submitted_at":"2017-10-28T02:48:45Z","abstract_excerpt":"We formulate a $q$-Schur algebra associated to an arbitrary $W$-invariant finite set $X_{\\texttt f}$ of integral weights for a complex simple Lie algebra with Weyl group $W$. We establish a $q$-Schur duality between the $q$-Schur algebra and Hecke algebra associated to $W$. We then realize geometrically the $q$-Schur algebra and duality, and construct a canonical basis for the $q$-Schur algebra with positivity. With suitable choices of $X_{\\texttt f}$ in classical types, we recover the $q$-Schur algebras in the literature. Our $q$-Schur algebras are closely related to the category $\\mathcal O$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10375","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/1710.10375/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":"1710.10375","created_at":"2026-07-05T03:57:22.493737+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.10375v3","created_at":"2026-07-05T03:57:22.493737+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10375","created_at":"2026-07-05T03:57:22.493737+00:00"},{"alias_kind":"pith_short_12","alias_value":"PCIXJEDO4KNA","created_at":"2026-07-05T03:57:22.493737+00:00"},{"alias_kind":"pith_short_16","alias_value":"PCIXJEDO4KNACBGB","created_at":"2026-07-05T03:57:22.493737+00:00"},{"alias_kind":"pith_short_8","alias_value":"PCIXJEDO","created_at":"2026-07-05T03:57:22.493737+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/PCIXJEDO4KNACBGBFGQMKWJKBA","json":"https://pith.science/pith/PCIXJEDO4KNACBGBFGQMKWJKBA.json","graph_json":"https://pith.science/api/pith-number/PCIXJEDO4KNACBGBFGQMKWJKBA/graph.json","events_json":"https://pith.science/api/pith-number/PCIXJEDO4KNACBGBFGQMKWJKBA/events.json","paper":"https://pith.science/paper/PCIXJEDO"},"agent_actions":{"view_html":"https://pith.science/pith/PCIXJEDO4KNACBGBFGQMKWJKBA","download_json":"https://pith.science/pith/PCIXJEDO4KNACBGBFGQMKWJKBA.json","view_paper":"https://pith.science/paper/PCIXJEDO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.10375&json=true","fetch_graph":"https://pith.science/api/pith-number/PCIXJEDO4KNACBGBFGQMKWJKBA/graph.json","fetch_events":"https://pith.science/api/pith-number/PCIXJEDO4KNACBGBFGQMKWJKBA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PCIXJEDO4KNACBGBFGQMKWJKBA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PCIXJEDO4KNACBGBFGQMKWJKBA/action/storage_attestation","attest_author":"https://pith.science/pith/PCIXJEDO4KNACBGBFGQMKWJKBA/action/author_attestation","sign_citation":"https://pith.science/pith/PCIXJEDO4KNACBGBFGQMKWJKBA/action/citation_signature","submit_replication":"https://pith.science/pith/PCIXJEDO4KNACBGBFGQMKWJKBA/action/replication_record"}},"created_at":"2026-07-05T03:57:22.493737+00:00","updated_at":"2026-07-05T03:57:22.493737+00:00"}