{"paper":{"title":"Satake diagrams and real structures on spherical varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dmitri Akhiezer","submitted_at":"2014-03-04T06:29:10Z","abstract_excerpt":"With each antiholomorphic involution $\\sigma $ of a connected complex semisimple Lie group $G$ we associate an automorphism $\\epsilon_\\sigma$ of the Dynkin diagram. The definition of $\\epsilon_\\sigma$ is given in terms of the Satake diagram of $\\sigma $. Let $H \\subset G$ be a self-normalizing spherical subgroup. If $\\epsilon_\\sigma ={\\rm id}$ then we prove the uniqueness and existence of a $\\sigma $-equivariant real structure on $G/H$ and on the wonderful completion of $G/H$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0698","kind":"arxiv","version":4},"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"}