{
  "abstract": "For the symmetric pair $(\\mathrm{GL}_n(\\mathbb C),\\mathrm{GL}_n(\\mathbb R))$, we compute the exact Flicker--Rallis period of a distinguished vector in a cohomological minimal $U(n)$-type, normalized by the Gel'fand--Tsetlin pairing of Hara--Miyazaki--Namikawa. Our main tool is a weight-independent identity between the Whittaker period and a compact $O(n)$-average. We determine the proportionality constant using the archimedean newform formula of Humphries--Jo, and evaluate the compact functional on the normalized distinguished vector. This yields an explicit formula for the Flicker--Rallis period for every cohomological weight.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31018",
  "author_total": 1,
  "authors": [
    {
      "name": "Zheng Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cdkzvf3c6tdxw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31018",
  "fulltext_url": null,
  "id": "cdkzvf3c6tdxw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31018",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7223294446",
  "pdf_url": "https://arxiv.org/pdf/2610.31018",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cdkzvf3c6tdxw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.31018",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31018"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Exact Archimedean Flicker--Rallis Periods on Cohomological Minimal $K$-Types",
  "title_text": "Exact Archimedean Flicker--Rallis Periods on Cohomological Minimal K-Types",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/cdkzvf3c6tdxw",
  "venue": "arXiv",
  "versions": []
}