{
  "abstract": "Let $F$ be a non-Archimedean local field of characteristic zero, let $D/F$ be the quaternion division algebra, and put $G_n = GL_n(D)$ and $H_n = Sp_n(D)$. We prove Prasad's revised conjecture on tempered representations with symplectic period. If $ρ$ is a unitary $H_r$-distinguished supercuspidal representation and $δ_m(ρ)$ denotes the generalized Steinberg representation associated to $ρ$, set $B_0(ρ) = ρ, B_m(ρ) = δ_{m+1}(ρ) \\times δ_m(ρ), m \\geq 1.$ We prove that an irreducible tempered representation $π$ of $G_n$ is $H_n$-distinguished if and only if $π$ is isomorphic to the product over $i$ of $B_{m_i}(ρ_i),$ where each $ρ_i$ is a unitary distinguished supercuspidal representation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05364",
  "author_total": 1,
  "authors": [
    {
      "name": "Mahendra Kumar Verma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6b7y55dbjan0q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05364",
  "fulltext_url": null,
  "id": "6b7y55dbjan0q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05364",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7220660149",
  "pdf_url": "https://arxiv.org/pdf/2610.05364",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6b7y55dbjan0q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05364",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05364"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Tempered Symplectic Distinction For Quaternionic $GL_n(D)$: A Conjecture of PRASAD",
  "title_text": "Tempered Symplectic Distinction For Quaternionic GL_n(D): A Conjecture of PRASAD",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/6b7y55dbjan0q",
  "venue": "arXiv",
  "versions": []
}