{"paper":{"title":"Invariant convex sets in polar representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"Alessandro Ghigi, Leonardo Biliotti, Peter Heinzner","submitted_at":"2014-11-21T22:12:53Z","abstract_excerpt":"We study a compact invariant convex set $E$ in a polar representation of a compact Lie group. Polar rapresentations are given by the adjoint action of $K$ on $\\mathfrak{p}$, where $K$ is a maximal compact subgroup of a real semisimple Lie group $G$ with Lie algebra $\\mathfrak{g} = \\mathfrak{k} \\oplus \\mathfrak{p}$. If $\\mathfrak{a} \\subset \\mathfrak{p}$ is a maximal abelian subalgebra, then $P=E\\cap \\mathfrak{a}$ is a convex set in $\\mathfrak{a}$. We prove that up to conjugacy the face structure of $E$ is completely determined by that of $P$ and that a face of $E$ is exposed if and only if the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6041","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"}