{"paper":{"title":"The image of the Lepowsky homomorphism for the group $F_4$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Alfredo Brega, Juan Tirao, Leandro Cagliero","submitted_at":"2011-07-04T15:15:42Z","abstract_excerpt":"Let $G_o$ be a semisimple Lie group, let $K_o$ be a maximal compact subgroup of $G_o$ and let $\\mathfrak{k}\\subset\\mathfrak{g}$ denote the complexification of their Lie algebras. Let $G$ be the adjoint group of $\\mathfrak{g}$ and let $K$ be the connected Lie subgroup of $G$ with Lie algebra $ad(\\mathfrak{k})$. If $U(\\mathfrak{g})$ is the universal enveloping algebra of $\\mathfrak{g}$ then $U(\\mathfrak{g})^K$ will denote the centralizer of $K$ in $U(\\mathfrak{g})$. Also let $P:U(\\mathfrak{g})\\longrightarrow U(\\mathfrak{k})\\otimes U(\\mathfrak{a})$ be the projection map corresponding to the direc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0651","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"}