{"paper":{"title":"A connection between minimal nilpotent orbits of types A and D via Hamiltonian reduction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The affine closure of the cotangent bundle to the minimal nilpotent orbit in type A equals a C* Hamiltonian reduction of the minimal nilpotent orbit closure in type D.","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Baohua Fu, Jie Liu","submitted_at":"2026-05-05T06:52:27Z","abstract_excerpt":"We establish a novel connection between the minimal nilpotent orbit $\\mathbb{O}_n$ in $\\mathfrak{sl}_n$ and the minimal nilpotent orbit closure $\\overline{\\mathbf{O}}_n$ in $\\mathfrak{so}_{2n+2}$, which differs from the shared-orbit paradigm of Brylinski and Kostant, where no direct type-A--type-D relation appears. More precisely, we show that the affine closure of the cotangent bundle $\\overline{T^*\\mathbb{O}_n}^{\\mathrm{aff}}$ is isomorphic to a $\\mathbb{C}^*$-Hamiltonian reduction of $\\overline{\\mathbf{O}}_n$. This provides a quasi-classical analogue of a quantum result of Levasseur and Sta"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"the affine closure of the cotangent bundle T*O_n^aff is isomorphic to a C*-Hamiltonian reduction of the minimal nilpotent orbit closure O_n in so_{2n+2}","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the chosen C* action on the orbit closure admits a well-defined moment map whose Hamiltonian reduction yields an isomorphism to the affine cotangent bundle closure, and that the subsequent geometric analysis correctly detects the non-existence of a symplectic resolution.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The affine closure of the cotangent bundle of the minimal nilpotent orbit O_n in sl_n is isomorphic to a C*-Hamiltonian reduction of the minimal nilpotent orbit closure in so_{2n+2}.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The affine closure of the cotangent bundle to the minimal nilpotent orbit in type A equals a C* Hamiltonian reduction of the minimal nilpotent orbit closure in type D.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"3c5242bf5116248240601c60c8a3821e7f811b49020ffd690b5b191c4d67b942"},"source":{"id":"2605.03421","kind":"arxiv","version":2},"verdict":{"id":"28268538-dfab-4336-a472-9850ca0d3300","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-07T12:42:46.988673Z","strongest_claim":"the affine closure of the cotangent bundle T*O_n^aff is isomorphic to a C*-Hamiltonian reduction of the minimal nilpotent orbit closure O_n in so_{2n+2}","one_line_summary":"The affine closure of the cotangent bundle of the minimal nilpotent orbit O_n in sl_n is isomorphic to a C*-Hamiltonian reduction of the minimal nilpotent orbit closure in so_{2n+2}.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the chosen C* action on the orbit closure admits a well-defined moment map whose Hamiltonian reduction yields an isomorphism to the affine cotangent bundle closure, and that the subsequent geometric analysis correctly detects the non-existence of a symplectic resolution.","pith_extraction_headline":"The affine closure of the cotangent bundle to the minimal nilpotent orbit in type A equals a C* Hamiltonian reduction of the minimal nilpotent orbit closure in type D."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.03421/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-20T01:01:22.125205Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T15:25:37.985795Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"55c475fbb5115824a8640b02bbc2d6b58b56dd65356ad89ace9b7a67f76e7a7f"},"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"}