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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-"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1303.6661","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-03-26T21:04:47Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"9e70f3267f4c93d57ffa3707e39ab928963e277c5810b31b0cc5932e81a5eba4","abstract_canon_sha256":"a0c8b49345843a8318fe92928a9beee37aaa3e216a4d2b94824185b91e8e776f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:12.035079Z","signature_b64":"MqFxEm+MUSbckr0lFeaLnzG8dildO8KgIYMwu0HL3BU362jM2P1xcsOMLz52I1h0D7JIuLzuVL8pG+DNQ7V8Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a589cd0c8c374ac88a8ea0c4a905326767023d94000257d398fa20733dfe58c8","last_reissued_at":"2026-05-18T03:27:12.034325Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:12.034325Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1303.6661","created_at":"2026-05-18T03:27:12.034449+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.6661v2","created_at":"2026-05-18T03:27:12.034449+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.6661","created_at":"2026-05-18T03:27:12.034449+00:00"},{"alias_kind":"pith_short_12","alias_value":"UWE42DEMG5FM","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_16","alias_value":"UWE42DEMG5FMRCUO","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_8","alias_value":"UWE42DEM","created_at":"2026-05-18T12:28:02.375192+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UWE42DEMG5FMRCUOUDCKSBJSM5","json":"https://pith.science/pith/UWE42DEMG5FMRCUOUDCKSBJSM5.json","graph_json":"https://pith.science/api/pith-number/UWE42DEMG5FMRCUOUDCKSBJSM5/graph.json","events_json":"https://pith.science/api/pith-number/UWE42DEMG5FMRCUOUDCKSBJSM5/events.json","paper":"https://pith.science/paper/UWE42DEM"},"agent_actions":{"view_html":"https://pith.science/pith/UWE42DEMG5FMRCUOUDCKSBJSM5","download_json":"https://pith.science/pith/UWE42DEMG5FMRCUOUDCKSBJSM5.json","view_paper":"https://pith.science/paper/UWE42DEM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.6661&json=true","fetch_graph":"https://pith.science/api/pith-number/UWE42DEMG5FMRCUOUDCKSBJSM5/graph.json","fetch_events":"https://pith.science/api/pith-number/UWE42DEMG5FMRCUOUDCKSBJSM5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UWE42DEMG5FMRCUOUDCKSBJSM5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UWE42DEMG5FMRCUOUDCKSBJSM5/action/storage_attestation","attest_author":"https://pith.science/pith/UWE42DEMG5FMRCUOUDCKSBJSM5/action/author_attestation","sign_citation":"https://pith.science/pith/UWE42DEMG5FMRCUOUDCKSBJSM5/action/citation_signature","submit_replication":"https://pith.science/pith/UWE42DEMG5FMRCUOUDCKSBJSM5/action/replication_record"}},"created_at":"2026-05-18T03:27:12.034449+00:00","updated_at":"2026-05-18T03:27:12.034449+00:00"}