{
  "abstract": "We establish a unified fixed-point Grassmannian framework for the classical pseudo-Riemannian symmetric spaces from Berger's classification. For a classical group $G=\\mathop{\\mathrm{Aut}}(V,b)$, we identify $G$ with the open graph-like locus inside an ordinary or maximal-isotropic Grassmannian $\\overline{G}$. Natural involutions of $\\overline{G}$ are constructed via classical forms, compatible scalar structures, and subspace configurations. We explicitly describe the full fixed loci of these involutions in terms of classical Grassmannians. The corresponding graph-like fixed loci (or their signature strata) are identified, respectively, with the moduli spaces of classical forms, compatible scalar structures, and subspace configurations; these moduli spaces coincide with classical pseudo-Riemannian symmetric spaces. In summary, the 54 classical series are organized into four families: 10 group-type models, 7 classical-form Grassmannians, 20 scalar-structure Grassmannians, and 17 subspace-configuration Grassmannians.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36724",
  "author_total": 2,
  "authors": [
    {
      "name": "Yunxia Chen"
    },
    {
      "name": "Naichung Conan Leung"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4v6pcj0bevvkr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36724",
  "fulltext_url": null,
  "id": "4v6pcj0bevvkr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36724",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7224127680",
  "pdf_url": "https://arxiv.org/pdf/2610.36724",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4v6pcj0bevvkr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.36724",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36724"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Grassmannian Realizations of Classical Pseudo-Riemannian Symmetric Spaces",
  "title_text": "Grassmannian Realizations of Classical Pseudo-Riemannian Symmetric Spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/4v6pcj0bevvkr",
  "venue": "arXiv",
  "versions": []
}