{"paper":{"title":"Enhanced orbit embedding","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Kyo Nishiyama","submitted_at":"2014-10-09T02:30:37Z","abstract_excerpt":"Let $ \\tilde{G} $ be an algebraic group acting on a variety $ \\tilde{L} $, and $ G \\subset \\tilde{G} $ a subgroup which leaves a subvariety $ L \\subset \\tilde{L} $ stable. For a $ G $-orbit $ O_G = G u (u \\in L) $ in $ L $, we can associate an orbit $ O_{\\tilde{G}} = \\tilde{G} u $ of $ \\tilde{G} $ so that we get a map $ L/G \\to \\tilde{L}/\\tilde{G} $ between orbit spaces, though this map is usually not injective. In this note, when $ G $ is a symmetric subgroup arising from an involutive anti-automorphism, we give certain sufficient conditions for the map $ L/G \\to \\tilde{L}/\\tilde{G} $ to be i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2336","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"}