{"paper":{"title":"The Gelfand-Zeitlin integrable system and K-orbits on the flag variety","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Mark Colarusso, Sam Evens","submitted_at":"2011-11-11T21:15:55Z","abstract_excerpt":"In this expository paper, we provide an overview of the Gelfand-Zeiltin integrable system on the Lie algebra of $n\\times n$ complex matrices $\\fgl(n,\\C)$ introduced by Kostant and Wallach in 2006. We discuss results concerning the geometry of the set of strongly regular elements, which consists of the points where Gelfand-Zeitlin flow is Lagrangian. We use the theory of $K_{n}=GL(n-1,\\C)\\times GL(1,\\C)$-orbits on the flag variety $\\mathcal{B}_{n}$ of $GL(n,\\C)$ to describe the strongly regular elements in the nilfiber of the moment map of the system. We give an overview of the general theory o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2868","kind":"arxiv","version":1},"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"}