{"paper":{"title":"Eigenvalue Coincidences and $K$-orbits, I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Mark Colarusso, Sam Evens","submitted_at":"2013-03-26T21:04:47Z","abstract_excerpt":"We study the variety $\\mathfrak{g}(l)$ consisting of matrices $x \\in \\mathfrak{gl}(n,\\C)$ such that $x$ and its $n-1$ by $n-1$ cutoff $x_{n-1}$ share exactly $l$ eigenvalues, counted with multiplicity. We determine the irreducible components of $\\mathfrak{g}(l)$ by using the orbits of $GL(n-1,\\C)$ on the flag variety $\\B_n$ of $\\mathfrak{gl}(n,\\C)$. More precisely, let $\\mathfrak{b} \\in \\B_n$ be a Borel subalgebra such that the orbit $GL(n-1,\\C)\\cdot \\mathfrak{b}$ in $\\B_n$ has codimension $l$. Then we show that the set $Y_{\\fb}:= \\{\\Ad(g)(x): x\\in \\mathfrak{b} \\cap \\mathfrak{g}(l), g\\in GL(n-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6661","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"}