{"paper":{"title":"Simple endotrivial modules for linear, unitary and exceptional groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"Caroline Lassueur, Gunter Malle","submitted_at":"2015-01-02T13:39:04Z","abstract_excerpt":"Motivated by a recent result of Robinson showing that simple endotrivial modules essentially come from quasi-simple groups we classify such modules for finite special linear and unitary groups as well as for exceptional groups of Lie type. Our main tool is a lifting result for endotrivial modules obtained in a previous paper which allows us to apply character theoretic methods. As one application we prove that the $\\ell$-rank of quasi-simple groups possessing a faithful simple endotrivial module is at most 2. As a second application we complete the proof that principal blocks of finite simple "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00400","kind":"arxiv","version":1},"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"}