{
  "abstract": "Let $U$ be a Sylow $p$-subgroup in a classical group over a finite field with $q$ elements of characteristic $p$ large enough. The coadjoint orbits of the group $U$ play the key role in the description of irreducible complex characters of $U$. In the paper, we provide a classification of such orbits of pre-maximal dimension for symplectic groups and orbits of maximal dimension for orthogonal groups. As a corollary, we compute the number of all orbits mentioned above. It turned out that each of these numbers is a polynomial in $q - 1$ with integer non-negative coefficients, which agrees with the Isaacs' conjecture.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.27523",
  "author_total": 2,
  "authors": [
    {
      "name": "Mikhail Ignatev"
    },
    {
      "name": "Mikhail Venchakov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3szcj1wt91bxn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.27523",
  "fulltext_url": null,
  "id": "3szcj1wt91bxn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.27523",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7204819284",
  "pdf_url": "https://arxiv.org/pdf/2608.27523",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3szcj1wt91bxn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.27523",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.27523"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Orbits of maximal and submaximal dimension for Sylow $p$-subgroups of finite classical groups",
  "title_text": "Orbits of maximal and submaximal dimension for Sylow p-subgroups of finite classical groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/3szcj1wt91bxn",
  "venue": "arXiv",
  "versions": []
}