{
  "abstract": "We explicitly compute and parametrize the centralizers of elements, encompassing dege\\-ne\\-rate and unipotent ones, in the orthogonal, symplectic, and unitary gro\\-ups over the real and complex fields, including the indefinite cases. The same approach simultaneously yields the isotropy groups of $H$-skew-symme\\-tric, Hamiltonian, and $H$-Hermitian matrices under the adjoint representations of the corresponding classical groups. The resulting groups are conjugate to subgroups of nonsingular block matrices whose blocks exhibit a rectangular block Toeplitz structure.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05471",
  "author_total": 1,
  "authors": [
    {
      "name": "Tadej Starčič"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/89892rh6mv4zq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05471",
  "fulltext_url": null,
  "id": "89892rh6mv4zq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05471",
  "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.AG"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7220681530",
  "pdf_url": "https://arxiv.org/pdf/2610.05471",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/89892rh6mv4zq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05471",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05471"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Centralizers of elements in the orthogonal, symplectic and unitary groups",
  "title_text": "Centralizers of elements in the orthogonal, symplectic and unitary groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/89892rh6mv4zq",
  "venue": "arXiv",
  "versions": []
}