{"paper":{"title":"The modality of a Borel subgroup in a simple algebraic group of type $E_8$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Gerhard Roehrle, Peter Mosch, Simon Goodwin","submitted_at":"2018-02-09T09:04:52Z","abstract_excerpt":"Let $G$ be a simple algebraic group over an algebraically closed field $k$, where $\\mathrm{char}\\, k$ is either 0 or a good prime for $G$. We consider the modality $\\mathrm{mod}(B : \\mathfrak u)$ of the action of a Borel subgroup $B$ of $G$ on the Lie algebra $\\mathfrak u$ of the unipotent radical of $B$, and report on computer calculations used to show that $\\mathrm{mod}(B:\\mathfrak u) = 20$, when $G$ is of type $\\mathrm E_8$. This completes the determination of the values for $\\mathrm{mod}(B:\\mathfrak u)$ for $G$ of exceptional type."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.03175","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"}