{
  "abstract": "We use a gluing procedure introduced by Ginzburg to describe the relative Langlands dual of the hyperspherical Hamiltonian $(\\mathrm{GL}_n \\times \\mathrm{GL}_m)$-variety $T^*(\\mathrm{Hom}(\\mathbb{C}^m,\\mathbb{C}^n))$, and in particular the Rankin-Selberg case $m=n$. We show that the dual is isomorphic to the triangle part of Cherkis-Nakajima-Takayama bow varieties, recovering a result of Nakajima. Using this result, we give a new proof of a theorem of Braverman-Finkelberg-Nakajima describing the regular perverse sheaf in type $A$. Following a suggestion of Ginzburg, we explain how to modify the gluing so that the dual Hamiltonian variety of $T^*\\mathbf{N}$, for any gluable finite-dimensional representation $\\mathbf{N}$ of a complex reductive group $G$, is naturally equipped with an anti-symplectic involution, and give an explicit formula for this involution in the Rankin-Selberg case.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.22965",
  "author_total": 1,
  "authors": [
    {
      "name": "Bruno da Silveira Dias"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/agbyt3nbc3fbj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.22965",
  "fulltext_url": null,
  "id": "agbyt3nbc3fbj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.22965",
  "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": "W7171491732",
  "pdf_url": "https://arxiv.org/pdf/2607.22965",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/agbyt3nbc3fbj.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2607.22965",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.22965"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Rankin-Selberg duality via gluing",
  "title_text": "Rankin-Selberg duality via gluing",
  "type": "preprint",
  "updated_at": "2026-11-07T18:20:21Z",
  "url": "https://research.draconitic.com/paper/agbyt3nbc3fbj",
  "venue": "arXiv",
  "versions": []
}