{"paper":{"title":"Real group orbits on flag ind-varieties of $\\mathrm{SL}(\\infty,\\mathbb{C})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.AG","authors_text":"Ivan Penkov, Joseph A. Wolf, Mikhail V. Ignatyev","submitted_at":"2016-01-17T19:03:26Z","abstract_excerpt":"We consider the complex ind-group $G=\\mathrm{SL}(\\infty,\\mathbb{C})$ and its real forms $G^0=\\mathrm{SU}(\\infty,\\infty)$, $\\mathrm{SU}(p,\\infty)$, $\\mathrm{SL}(\\infty,\\mathbb{R})$, $\\mathrm{SL}(\\infty,\\mathbb{H})$. Our main objects of study are the $G^0$-orbits on an ind-variety $G/P$ for an arbitrary splitting parabolic ind-subgroup $P\\subset G$. We prove that the intersection of any $G^0$-orbit on $G/P$ with a finite-dimensional flag variety $G_n/P_n$ from a given exhaustion of $G/P$ via $G_n/P_n$ for $n\\to\\infty$, is a single $(G^0\\cap G_n)$-orbit. We also characterize all ind-varieties $G/"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04326","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"}