{"paper":{"title":"Nilpotent orbits, normality, and Hamiltonian group actions","license":"","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Bertram Kostant, Ranee Brylinski","submitted_at":"1992-04-01T00:00:00Z","abstract_excerpt":"Let $M$ be a $G$-covering of a nilpotent orbit in $\\g$ where $G$ is a complex semisimple Lie group and $\\g=\\text{Lie}(G)$. We prove that under Poisson bracket the space $R[2]$ of homogeneous functions on $M$ of degree 2 is the unique maximal semisimple Lie subalgebra of $R=R(M)$ containing $\\g$. The action of $\\g'\\simeq R[2]$ exponentiates to an action of the corresponding Lie group $G'$ on a $G'$-cover $M'$ of a nilpotent orbit in $\\g'$ such that $M$ is open dense in $M'$. We determine all such pairs $(\\g\\subset\\g')$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9204227","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"}