{
  "abstract": "We prove multiplicity at most one for the unitary similitude Ginzburg--Rallis model over local fields of characteristic zero, for both the quasi-split and non-quasi-split groups. The theorem holds for all irreducible smooth representations over non-Archimedean fields and all irreducible Casselman--Wallach representations over the real field. We first describe the decomposition into parabolic double cosets and compute the required stabilizers. Over a non-Archimedean field we use character obstructions, localization, and transpose symmetry. Over the real field we use a Casimir identity and explicit normal vectors to prove the corresponding statement for distributions with prescribed infinitesimal character. The Gelfand--Kazhdan criterion and a dualizing involution then give the multiplicity bound.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36294",
  "author_total": 3,
  "authors": [
    {
      "name": "Yuxuan Ge"
    },
    {
      "name": "Sagnik Mukherjee"
    },
    {
      "name": "Junyi Zhai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dvpxctpywxz81.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36294",
  "fulltext_url": null,
  "id": "dvpxctpywxz81",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36294",
  "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",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7224135874",
  "pdf_url": "https://arxiv.org/pdf/2610.36294",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dvpxctpywxz81.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.36294",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36294"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Multiplicity One for Unitary Ginzburg--Rallis Models over Local Fields",
  "title_text": "Multiplicity One for Unitary Ginzburg--Rallis Models over Local Fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/dvpxctpywxz81",
  "venue": "arXiv",
  "versions": []
}