{
  "abstract": "Let $K/\\mathbb{Q}_p$ be a finite extension of degree $n$ with $p\\geq3$, and let $D$ be the non-split quaternion algebra over $K$. We prove that every infinite-dimensional admissible smooth representation of $\\mathrm{GL}_2(K)$ or $D^\\times$ with a central character and satisfying a Casimir annihilation condition has Gelfand--Kirillov dimension $n$. As a corollary, every infinite-dimensional admissible Banach representation whose locally analytic vectors have an infinitesimal character has dimension $n$, strengthening Sorgdrager's bound to an equality. An appendix by Yongquan Hu proves that, when $K\\ne\\mathbb{Q}_p$ and the coefficient field is algebraically closed, the canonical diagram of an admissible supersingular representation satisfying the same Casimir annihilation condition is $(π,π,\\mathrm{id})$, as in the case of local fields of characteristic $p$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04350",
  "author_total": 2,
  "authors": [
    {
      "name": "Jiusi Zhao"
    },
    {
      "name": "Yongquan Hu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4mw1dryhw3g7w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04350",
  "fulltext_url": null,
  "id": "4mw1dryhw3g7w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04350",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04350",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4mw1dryhw3g7w.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.04350",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04350"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Ramified tori and Gelfand--Kirillov dimension of mod $p$ representations",
  "title_text": "Ramified tori and Gelfand--Kirillov dimension of mod p representations",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/4mw1dryhw3g7w",
  "venue": "arXiv",
  "versions": []
}