{"paper":{"title":"The Restricted Schatten-class Grassmannian $\\mathrm{Gr}_{\\mathrm{res}, p}(\\mathcal{H})$ as affine coadjoint orbit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP","math.OA"],"primary_cat":"math.FA","authors_text":"Alice Barbora Tumpach, Amin Tahiri","submitted_at":"2026-05-21T14:03:55Z","abstract_excerpt":"In this paper, we consider the restricted $p$-Schatten class Grassmannian $\\mathrm {Gr}_{{\\rm res}, p}(\\mathcal{H})$ consisting of infinite-dimensional and infinite codimensional subspaces $W$ of a polarized complex separable Hilbert space $\\mathcal{H} = \\mathcal{H}_+\\oplus \\mathcal{H}_-$ such that the orthogonal projection from $W$ onto $\\mathcal{H}_+$ is Fredholm and the orthogonal projection from $W$ onto $\\mathcal{H}_-$ is in the Schatten ideal $L_p$, $p\\geq 1$. The aim of this paper is to show that, for $1\\leq p\\leq 2$, the restricted $p$-Schatten class Grassmannian $\\mathrm {Gr}_{{\\rm re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22512","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/2605.22512/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"}