{"paper":{"title":"A new characterization of the exceptional Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"Erik Insko, Pamela Harris","submitted_at":"2014-03-13T00:44:46Z","abstract_excerpt":"For a simple Lie algebra, over $\\mathbb{C}$, we consider the weight which is the sum of all simple roots and denote it $\\tilde{\\alpha}$. We formally use Kostant's weight multiplicity formula to compute the \"dimension\" of the zero-weight space. In type $A_r$, $\\tilde{\\alpha}$ is the highest root, and therefore this dimension is the rank of the Lie algebra. In type $B_r$, this is the defining representation, with dimension equal to 1. In the remaining cases, the weight $\\tilde{\\alpha}$ is not dominant and is not the highest weight of an irreducible finite-dimensional representation. Kostant's we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3139","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"}