{
  "abstract": "Let $\\widetilde G$ be a nonlinear double cover of the real points of a connected, simply connected, semisimple complex group. In previous work, we introduced $\\prod_{ρ/2}^s(\\widetilde G)$, the set of genuine small representations with infinitesimal character $ρ/2$ in the simply laced setting, and showed that, when $G$ is split, these representations are exhausted by the Kazhdan--Patterson lift of the trivial representation. In this paper, we consider nonsplit real Spin groups of type $D_n$. For each $ρ/2$-compatible genuine central character, we determine the irreducible constituents of $\\mathrm{Lift}_G^{\\widetilde G}(\\mathbb C)$. We also describe explicitly the relevant genuine small representations in terms of Langlands parameters. The nonsplit case exhibits a new phenomenon: the lift of the trivial representation need not exhaust $\\prod\\nolimits^s_{ρ/2}(\\widetilde G)$. For the families considered here, equality holds only for $\\widetilde{\\mathrm{Spin}}(2p+2,2p)$; in the other two families the lift is a proper subset, and in one case it is zero.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23675",
  "author_total": 1,
  "authors": [
    {
      "name": "Wan-Yu Tsai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e63br82pg68d8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23675",
  "fulltext_url": null,
  "id": "e63br82pg68d8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23675",
  "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": "W7214026542",
  "pdf_url": "https://arxiv.org/pdf/2609.23675",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e63br82pg68d8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23675",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23675"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Lift of the Trivial Representation: The Nonsplit Type $D$ Case",
  "title_text": "Lift of the Trivial Representation: The Nonsplit Type D Case",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/e63br82pg68d8",
  "venue": "arXiv",
  "versions": []
}