{"paper":{"title":"Lifting representations of finite reductive groups I: Semisimple conjugacy classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Jeffrey D. Adler, Joshua M. Lansky","submitted_at":"2011-06-04T03:20:32Z","abstract_excerpt":"Suppose that $\\tilde{G}$ is a connected reductive group defined over a field $k$, and $\\Gamma$ is a finite group acting via $k$-automorphisms of $\\tilde{G}$ satisfying a certain quasi-semisimplicity condition. Then the connected part of the group of $\\Gamma$-fixed points in $\\tilde{G}$ is reductive. We axiomatize the main features of the relationship between this fixed-point group and the pair $(\\tilde{G},\\Gamma)$, and consider any group $G$, not just the $\\Gamma$-fixed points of $\\tilde{G}$, satisfying the axioms. (In fact, the axioms do not require $\\Gamma$ to act on all of $\\tilde{G}$.) If "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0786","kind":"arxiv","version":6},"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"}