{
  "abstract": "Let $F$ be a finite extension of $\\mathbb Q_p$, for any prime $p$, and let $L/F$ be a ramified quadratic extension. We compute the spaces of $\\mathcal O_L^\\times$-equivariant linear forms on the representation $\\operatorname{ind}^G_{KZ}σ/(Φ-λ)$. The only nonzero cases arise from one-dimensional quotients. Consequently, the restriction of an infinite-dimensional irreducible smooth mod $p$ representation of $\\operatorname{GL}_2(F)$ with a central character to $\\mathcal O_L^\\times$ has no character quotient. We apply this vanishing result to show that a finite tensor product of smooth mod $p$ representations of $\\operatorname{GL}_2(F)$ admits no nonzero invariant linear form whenever at least one factor is infinite-dimensional and irreducible with a central character.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26541",
  "author_total": 3,
  "authors": [
    {
      "name": "Hao Liu"
    },
    {
      "name": "Haoran Wang"
    },
    {
      "name": "Yuting Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3r621yrz3j2xb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26541",
  "fulltext_url": null,
  "id": "3r621yrz3j2xb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26541",
  "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"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7223045438",
  "pdf_url": "https://arxiv.org/pdf/2610.26541",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3r621yrz3j2xb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.26541",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26541"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On multilinear forms for mod $p$ representations of $\\operatorname{GL}_2$ over a $p$-adic field",
  "title_text": "On multilinear forms for mod p representations of GL_2 over a p-adic field",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/3r621yrz3j2xb",
  "venue": "arXiv",
  "versions": []
}