{"paper":{"title":"Ind-varieties of generalized flags: a survey of results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Ivan Penkov, Mikhail V. Ignatyev","submitted_at":"2017-01-30T04:21:44Z","abstract_excerpt":"This is a review of results on the structure of the homogeneous ind-varieties $G/P$ of the ind-groups $G=\\mathrm{GL}_{\\infty}(\\mathbb{C})$, $\\mathrm{SL}_{\\infty}(\\mathbb{C})$, $\\mathrm{SO}_{\\infty}(\\mathbb{C})$, $\\mathrm{Sp}_{\\infty}(\\mathbb{C})$, subject to the condition that $G/P$ is a inductive limit of compact homogeneous spaces $G_n/P_n$. In this case the subgroup $P\\subset G$ is a splitting parabolic subgroup of $G$, and the ind-variety $G/P$ admits a \"flag realization\". Instead of ordinary flags, one considers generalized flags which are, generally infinite, chains $\\mathcal{C}$ of subs"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08478","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"}