{
  "abstract": "Let $F/\\mathbf Q_p$ and $E/\\mathbf Q_p$ be finite extensions, and let $G=\\mathrm{GL}_2(F)$ or $D_F^\\times$, where $D_F$ is the quaternion division algebra over $F$. Let $Π$ be an admissible Banach $E$-representation of $G$ whose locally $\\mathbf Q_p$-analytic vectors $Π^{\\mathrm{an}}$ have an infinitesimal character. If $p>2$ or $F=\\mathbf Q_p$, we prove that $Π^{\\mathrm{an}}$ and $Π$ have finite length in their respective admissible categories.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15841",
  "author_total": 1,
  "authors": [
    {
      "name": "Pengcheng Ding"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0rq2z2ftsp8ey.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15841",
  "fulltext_url": null,
  "id": "0rq2z2ftsp8ey",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15841",
  "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",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7221789561",
  "pdf_url": "https://arxiv.org/pdf/2610.15841",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0rq2z2ftsp8ey.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15841",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15841"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Finite Length of Locally Analytic Vectors for $\\mathrm{GL}_2(F)$ and $D_F^\\times$",
  "title_text": "Finite Length of Locally Analytic Vectors for GL_2(F) and D_F^×",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/0rq2z2ftsp8ey",
  "venue": "arXiv",
  "versions": []
}