{"paper":{"title":"Forced gradings and the Humphreys-Verma conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Brian Parshall, Leonard Scott","submitted_at":"2012-11-30T21:51:03Z","abstract_excerpt":"Let $G$ be a semisimple, simply connected algebraic group defined and split over a prime field ${\\mathbb F}_p$ of positive characteristic. For a positive integer $r$, let $G_r$ be the $r$th Frobenius kernel of $G$. Let $Q$ be a projective indecomposable (rational) $G_r$-module. The well-known Humprheys-Verma conjecture (cf. \\cite{Ballard}) asserts that the $G_r$-action on $Q$ lifts to an rational action of $G$ on $Q$. For $p\\geq 2h-2$ (where $h$ is the Coxeter number of $G$), this conjecture was proved by Jantzen in 1980, improving on early work of Ballard. However, it remains open for general"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0021","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"}