{"paper":{"title":"On commuting varieties of parabolic subalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Russell Goddard, Simon M. Goodwin","submitted_at":"2016-06-07T18:53:41Z","abstract_excerpt":"Let $G$ be a connected reductive algebraic group over an algebraically closed field $k$, and assume that the characteristic of $k$ is zero or a pretty good prime for $G$. Let $P$ be a parabolic subgroup of $G$ and let $\\mathfrak p$ be the Lie algebra of $P$. We consider the commuting variety $\\mathcal C(\\mathfrak p) = \\{(X,Y) \\in \\mathfrak p \\times \\mathfrak p \\mid [X,Y] = 0\\}$. Our main theorem gives a necessary and sufficient condition for irreducibility of $\\mathcal C(\\mathfrak p)$ in terms of the modality of the adjoint action of $P$ on the nilpotent variety of $\\mathfrak p$. As a conseque"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02262","kind":"arxiv","version":3},"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"}