{"paper":{"title":"On the algebraic set of singular elements in a complex simple Lie algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Bertram Kostant, Nolan Wallach","submitted_at":"2010-11-14T23:52:46Z","abstract_excerpt":"Let $G$ be a complex simple Lie group and let $\\g = \\hbox{\\rm Lie}\\,G$. Let $S(\\g)$ be the $G$-module of polynomial functions on $\\g$ and let $\\hbox{\\rm Sing}\\,\\g$ be the closed algebraic cone of singular elements in $\\g$. Let ${\\cal L}\\s S(\\g)$ be the (graded) ideal defining $\\hbox{\\rm Sing}\\,\\g$ and let $2r$ be the dimension of a $G$-orbit of a regular element in $\\g$. Then ${\\cal L}^k = 0$ for any $k<r$. On the other hand, there exists a remarkable $G$-module $M\\s {\\cal L}^r$ which already defines $\\hbox{\\rm Sing}\\,\\g$. The main results of this paper are a determination of the structure of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3267","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"}