{
  "abstract": "We characterize the standard modules of $\\GL_{2m}(\\C)$ that are distinguished by $\\GL_m(\\HH)$. Let $δ_1,\\dots, δ_{2m}$ be characters of $\\mathbb{C}^\\times$. Assume that $S = δ_1 \\times \\cdots \\times δ_{2m}$ is a standard module of $\\GL_{2m}(\\mathbb{C})$. For each $i$, define ${δ_i^*} (z) = δ_i(\\overline{z})^{-1}$ for $ z \\in \\mathbb{C}^\\times$. In particular, we conclude that a standard module for $\\GL_{2m}(\\mathbb{C})$ is distinguished by $\\GL_{m}(\\mathbb{H})$ if and only if there exists an involution $p\\in S_{2m}$ without fixed points such that $δ_{p(i)}=δ_i^*$ for every $i$. We first verify the hypotheses of the multiplicity estimate theorem of Suzuki and Tamori in \\cite{ST}. The orbit calculation of Matringe, Offen, and Yang in \\cite{MOYglobal} then gives the necessary condition and a dimension bound. Then local intertwining periods prove sufficiency.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10483",
  "author_total": 2,
  "authors": [
    {
      "name": "Alan Xuelun Hou"
    },
    {
      "name": "Tudor Popescu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d15gyczeh90em.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10483",
  "fulltext_url": null,
  "id": "d15gyczeh90em",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10483",
  "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",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7212115852",
  "pdf_url": "https://arxiv.org/pdf/2609.10483",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d15gyczeh90em.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:16Z",
      "native_id": "2609.10483",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10483"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Distinguished standard modules for $\\mathrm{GL}_{2m}(\\mathbb{C})/\\mathrm{GL}_m(\\mathbb{H})$",
  "title_text": "Distinguished standard modules for GL_2m(ℂ)/GL_m(ℍ)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:16Z",
  "url": "https://research.draconitic.com/paper/d15gyczeh90em",
  "venue": "arXiv",
  "versions": []
}