{
  "abstract": "We investigate the structure of locally analytic representations of $p$-adic groups, and establish a sufficient condition for the irreducibility of locally analytic vectors in certain Banach representations of $D^\\times$, where $D$ is the quaternion division algebra over $\\mathbb{Q}_p$. As an application, we prove that $\\mathrm{JL}(ρ)^{\\mathrm{an}}/\\mathrm{JL}(ρ)^{1\\text{-}\\mathrm{alg}}$ is a topologically irreducible locally analytic representation of $D^\\times$ under certain genericity conditions on $ρ$. Here $\\mathrm{JL}(ρ)$ is the $ρ(-1)$-multiplicity space in the image of $Π(ρ)$ under Scholze's functor, and $Π(ρ)$ is the representation associated to $ρ$ by the $p$-adic local Langlands correspondence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04514",
  "author_total": 1,
  "authors": [
    {
      "name": "Yu Xiao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0v8za0ar6wds6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04514",
  "fulltext_url": null,
  "id": "0v8za0ar6wds6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04514",
  "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.NT"
    ],
    [
      "arxiv",
      "math.RT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04514",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0v8za0ar6wds6.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.04514",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04514"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the Irreducibility of Locally Analytic Vectors in Certain Banach Representations of $D^\\times$",
  "title_text": "On the Irreducibility of Locally Analytic Vectors in Certain Banach Representations of D^×",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/0v8za0ar6wds6",
  "venue": "arXiv",
  "versions": []
}