{"paper":{"title":"Irreducible representations of simple algebraic groups in which a unipotent element is represented by a matrix with single non-trivial Jordan block","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alexandre Zalesski, Donna Testerman","submitted_at":"2016-12-31T15:55:24Z","abstract_excerpt":"In this paper we prove the following result.\n  Let $G$ be a simply connected simple linear algebraic group of exceptional Lie type over an algebraically closed field $F$ of characteristic $p\\geq 0$, and let $u\\in G$ be a nonidentity unipotent element. Let $\\phi$ be a non-trivial irreducible representation of $G$.\n  Then the Jordan normal form of $\\phi(u)$ contains at most one non-trivial block if and only if $G$ is of type $G_2$, $u$ is a regular unipotent element and $\\dim \\phi\\leq 7$.\n  Note that the irreducible representations of the simple classical algebraic groups in which a non-trivial "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00125","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"}