{"paper":{"title":"Nilpotent subspaces and nilpotent orbits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Dmitri Panyushev, Oksana Yakimova","submitted_at":"2016-01-13T14:29:27Z","abstract_excerpt":"Let $G$ be a semisimple algebraic group with Lie algebra $\\mathfrak g$. For a nilpotent $G$-orbit $\\mathcal O\\subset\\mathfrak g$, let $d_\\mathcal O$ denote the maximal dimension of a subspace $V\\subset \\mathfrak g$ that is contained in the closure of $\\mathcal O$. In this note, we prove that $d_\\mathcal O \\le \\frac{1}{2}\\dim\\mathcal O$ and this upper bound is attained if and only if $\\mathcal O$ is a Richardson orbit. Furthermore, if $V$ is $B$-stable and $\\dim V= \\frac{1}{2}\\dim\\mathcal O$, then $V$ is the nilradical of a polarisation of $\\mathcal O$. Every nilpotent orbit closure has a disti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.03264","kind":"arxiv","version":2},"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"}