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These bases are not equivalent and we show that the transition matrix S(\\lambda) between the two is the identity at u = 0 and u = \\infty. To prove this, we first prove a similar property for the transition matrices \\tilde{T}, \\tilde{T}' between the Kazhdan-Lusztig bases and their projected counterparts \\{\\tilde{C}_w\\}_{w \\in \\S_r}, \\{\\tilde{C}'_w\\}_{w"},"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":"1102.1453","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-02-07T22:10:00Z","cross_cats_sorted":[],"title_canon_sha256":"cb5633efa8179b2ef99a677b21529eb7da1f0855a2aa5332c37f1e1ee0fc14e8","abstract_canon_sha256":"c834ca78b1ae119366e3ac996bacfe17bea8c9570922ad04d504c217bcab3043"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:09.956087Z","signature_b64":"LYyz6ED97xD5FyQS09fIDbYuNc5wk3u2ez9BuQ37PWL1SgNcA6RHUKgBMjPP8o7KcrWLA7dPtlLUNrgKpzhoDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af8621cebdd6c1b0244e22449f1a58f3c532c5b6171da742c6ca621363a67433","last_reissued_at":"2026-05-18T03:05:09.955440Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:09.955440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum Schur-Weyl duality and projected canonical bases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jonah Blasiak","submitted_at":"2011-02-07T22:10:00Z","abstract_excerpt":"Let \\H_r be the generic type A Hecke algebra defined over \\ZZ[u, u^{-1}]. The Kazhdan-Lusztig bases \\{C_w\\}_{w \\in \\S_r} and \\{C'_w\\}_{w \\in \\S_r} of \\H_r give rise to two different bases of the Specht module M_\\lambda, \\lambda \\vdash r, of \\H_r. These bases are not equivalent and we show that the transition matrix S(\\lambda) between the two is the identity at u = 0 and u = \\infty. To prove this, we first prove a similar property for the transition matrices \\tilde{T}, \\tilde{T}' between the Kazhdan-Lusztig bases and their projected counterparts \\{\\tilde{C}_w\\}_{w \\in \\S_r}, \\{\\tilde{C}'_w\\}_{w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1453","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":""},"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":"1102.1453","created_at":"2026-05-18T03:05:09.955539+00:00"},{"alias_kind":"arxiv_version","alias_value":"1102.1453v3","created_at":"2026-05-18T03:05:09.955539+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.1453","created_at":"2026-05-18T03:05:09.955539+00:00"},{"alias_kind":"pith_short_12","alias_value":"V6DCDTV523A3","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_16","alias_value":"V6DCDTV523A3AJCO","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_8","alias_value":"V6DCDTV5","created_at":"2026-05-18T12:26:42.757692+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/V6DCDTV523A3AJCOEJCJ6GSY6P","json":"https://pith.science/pith/V6DCDTV523A3AJCOEJCJ6GSY6P.json","graph_json":"https://pith.science/api/pith-number/V6DCDTV523A3AJCOEJCJ6GSY6P/graph.json","events_json":"https://pith.science/api/pith-number/V6DCDTV523A3AJCOEJCJ6GSY6P/events.json","paper":"https://pith.science/paper/V6DCDTV5"},"agent_actions":{"view_html":"https://pith.science/pith/V6DCDTV523A3AJCOEJCJ6GSY6P","download_json":"https://pith.science/pith/V6DCDTV523A3AJCOEJCJ6GSY6P.json","view_paper":"https://pith.science/paper/V6DCDTV5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1102.1453&json=true","fetch_graph":"https://pith.science/api/pith-number/V6DCDTV523A3AJCOEJCJ6GSY6P/graph.json","fetch_events":"https://pith.science/api/pith-number/V6DCDTV523A3AJCOEJCJ6GSY6P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V6DCDTV523A3AJCOEJCJ6GSY6P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V6DCDTV523A3AJCOEJCJ6GSY6P/action/storage_attestation","attest_author":"https://pith.science/pith/V6DCDTV523A3AJCOEJCJ6GSY6P/action/author_attestation","sign_citation":"https://pith.science/pith/V6DCDTV523A3AJCOEJCJ6GSY6P/action/citation_signature","submit_replication":"https://pith.science/pith/V6DCDTV523A3AJCOEJCJ6GSY6P/action/replication_record"}},"created_at":"2026-05-18T03:05:09.955539+00:00","updated_at":"2026-05-18T03:05:09.955539+00:00"}