{"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"}