{"paper":{"title":"Eigenvalue Coincidences and Multiplicity Free Spherical Pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Mark Colarusso, Sam Evens","submitted_at":"2014-10-15T01:05:11Z","abstract_excerpt":"In recent work, we related the structure of subvarieties of $n\\times n$ complex matrices defined by eigenvalue coincidences to $GL(n-1,\\mathbb{C})$-orbits on the flag variety of $\\mathfrak{gl}(n,\\mathbb{C})$. In the first part of this paper, we extend these results to the complex orthogonal Lie algebra $\\mathfrak{g}=\\mathfrak{so}(n,\\mathbb{C})$. In the second part of the paper, we use these results to study the geometry and invariant theory of the $K$-action on $\\mathfrak{g}$, in the cases where $(\\mathfrak{g}, K)$ is $(\\mathfrak{gl}(n,\\mathbb{C}), GL(n-1,\\mathbb{C}))$ or $(\\mathfrak{so}(n,\\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3901","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"}