{
  "abstract": "We prove multiplicity one for a linear spherical pair associated with $\\mathrm{GL}_4(F)\\times\\mathrm{GL}_2(F)$ and its unitary similitude analogue associated with $\\mathrm{GU}(2,2)(F)\\times\\mathrm{GU}(1,1)(F)$. Both results hold for all irreducible admissible representations over non-Archimedean local fields of characteristic zero. Generalized Harish-Chandra descent reduces the proofs to the analysis of closed orbits and their normal representations. The unitary proof combines reductions to the linear case with a rational classification of closed orbits and a separate analysis of the remaining normal representations. We also establish multiplicity one for unitary Shalika periods of $\\mathrm{GU}(2,2)(F)$ with arbitrary irreducible admissible coefficients. A theta-period identity relates these periods to the unitary spherical pair. By varying the splitting character, we prove that every irreducible admissible representation of $\\mathrm{GU}(2,2)(F)$ occurs as a quotient of a suitable big theta lift, allowing the multiplicity-one bound to pass to the Shalika periods. The linear argument also recovers Rallis's multiplicity-one theorem for twisted Jacquet modules of $\\mathrm{GL}_4(F)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02670",
  "author_total": 1,
  "authors": [
    {
      "name": "Yuxuan Ge"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ahbcpxbazm9a8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02670",
  "fulltext_url": null,
  "id": "ahbcpxbazm9a8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02670",
  "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/2611.02670",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ahbcpxbazm9a8.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02670",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02670"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Multiplicity one for a linear spherical pair and its unitary analogue",
  "title_text": "Multiplicity one for a linear spherical pair and its unitary analogue",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/ahbcpxbazm9a8",
  "venue": "arXiv",
  "versions": []
}