{"paper":{"title":"On commuting varieties of nilradicals of Borel subalgebras of reductive Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Gerhard Roehrle, Simon Goodwin","submitted_at":"2012-09-06T14:16:42Z","abstract_excerpt":"Let $G$ be a connected reductive algebraic group defined over an algebraically closed field $\\mathbbm k$ of characteristic zero. We consider the commuting variety $\\mathcal C(\\mathfrak u)$ of the nilradical $\\mathfrak u$ of the Lie algebra $\\mathfrak b$ of a Borel subgroup $B$ of $G$. In case $B$ acts on $\\mathfrak u$ with only a finite number of orbits, we verify that $\\mathcal C(\\mathfrak u)$ is equidimensional and that the irreducible components are in correspondence with the {\\em distinguished} $B$-orbits in $\\mathfrak u$. We observe that in general $\\mathcal C(\\mathfrak u)$ is not equidim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1289","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"}