{"paper":{"title":"Extending Hecke endomorphism algebras at roots of unity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Brian Parshall, Jie Du, Leonard Scott","submitted_at":"2015-01-26T16:55:03Z","abstract_excerpt":"The (Iwahori-)Hecke algebra in the title is a $q$-deformation $\\sH$ of the group algebra of a finite Weyl group $W$. The algebra $\\sH$ has a natural enlargement to an endomorphism algebra $\\sA=\\End_\\sH(\\sT)$ where $\\sT$ is a $q$-permutation module. In type $A_n$ (i.e., $W\\cong {\\mathfrak S}_{n+1}$), the algebra $\\sA$ is a $q$-Schur algebra which is quasi-hereditary and plays an important role in the modular representation of the finite groups of Lie type. In other types, $\\sA$ is not always quasi-hereditary, but the authors conjectured 20 year ago that $\\sT$ can be enlarged to an $\\sH$-module "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06481","kind":"arxiv","version":2},"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"}