{"paper":{"title":"A proof of the first Kac-Weisfeiler conjecture in large characteristics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Akaki Tikaradze, Benjamin Martin, David Stewart, Lewis Topley","submitted_at":"2018-10-30T10:23:08Z","abstract_excerpt":"In 1971, Kac and Weisfeiler made two influential conjectures describing the dimensions of simple modules of a restricted Lie algebra $\\mathfrak{g}$. The first predicts the maximal dimension of simple $\\mathfrak{g}$-modules and in this paper we apply the Lefschetz principle and classical techniques from Lie theory to prove this conjecture for all restricted Lie subalgebras of $\\mathfrak{gl}_n(k)$ whenever $k$ is an algebraically closed field of characteristic $p \\gg n$. As a consequence we deduce that the conjecture holds for the the Lie algebra of a group scheme when specialised to an algebrai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12632","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"}