{"paper":{"title":"A complete description of the antipodal set of most symmetric spaces of compact type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jonas Beyrer","submitted_at":"2016-03-29T15:45:34Z","abstract_excerpt":"It is known that the antipodal set of a Riemannian symmetric space of compact type $G / K$ consists of a union of $K$-orbits. We determine the dimensions of these $K$-orbits of most irreducible symmetric spaces of compact type. The symmetric spaces we are not going to deal with are those with restricted root system $\\mathfrak{a}_r$ and a non-trivial fundamental group, which is not isomorphic to $\\mathbb{Z}_2$ or $\\mathbb{Z}_{r+1}$. For example, we show that the antipodal sets of the Lie groups $Spin(2r+1)\\:\\: r\\geq 5$, $E_8$ and $G_2$ consist only of one orbit which is of dimension $2r$, 128 a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08816","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"}