{"paper":{"title":"Collective superintegrable systems from the Guillemin--Sternberg torus action","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"L. Feher","submitted_at":"2026-08-03T08:22:41Z","abstract_excerpt":"We present a novel approach to the superintegrability of collective Hamiltonians invariant under a Hamiltonian action of a connected semisimple compact Lie group, $G$, on a symplectic manifold, $M$. By exploiting a Hamiltonian torus action that goes back to Guillemin and Sternberg [GS,1983], we demonstrate that the functional dimensions of $\\mathfrak{H} := \\mathcal{J}^*(C^\\infty(\\mathfrak{g}^*)^G)$, where $\\mathcal{J}: M \\to \\mathfrak{g}^*$ is the momentum map of the $G$ action, and its centralizer $\\mathfrak{F}$ in $C^\\infty(M)$ satisfy the equality $\\mathrm{ddim}(\\mathfrak{H}) + \\mathrm{ddim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.01878","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.01878/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}