{"paper":{"title":"Spherical nilpotent orbits and abelian subalgebras in isotropy representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jacopo Gandini, Paolo Papi, Pierluigi Moseneder Frajria","submitted_at":"2016-07-12T10:58:04Z","abstract_excerpt":"Let $G$ be a simply connected semisimple algebraic group with Lie algebra $\\mathfrak g$, let $G_0 \\subset G$ be the symmetric subgroup defined by an algebraic involution $\\sigma$ and let $\\mathfrak g_1 \\subset \\mathfrak g$ be the isotropy representation of $G_0$. Given an abelian subalgebra $\\mathfrak a$ of $\\mathfrak g$ contained in $\\mathfrak g_1$ and stable under the action of some Borel subgroup $B_0 \\subset G_0$, we classify the $B_0$-orbits in $\\mathfrak a$ and we characterize the sphericity of $G_0 \\mathfrak a$. Our main tool is the combinatorics of $\\sigma$-minuscule elements in the af"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03308","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"}