{
  "abstract": "Let $G$ be a $p$-adic classical group (orthogonal, symplectic, or unitary) and $π$ be an epipelagic representation of $G$ in the sense of Reeder-Yu. Using Mœglin's theory of extended cuspidal supports and Bushnell-Kutzko's theory of covering types, we determine explicitly the endoscopic lift of $π$ to the general linear group, whose Langlands dual expresses the dual group of $G$ as a complex matrix group, in terms of the inducing type of $π$ that extends the character of the first Moy-Prasad filtration subgroup defined by a stable functional. We interpret the inducing type of $π$ via Stevens' construction of supercuspidal representations by skew semisimple strata and introduce what we will call epipelagic strata, requiring only that the residual characteristic $p$ be odd. As an application, we reprove M. Oi's results on the endoscopic lifts of simple supercuspidal representations, in the sense of Gross-Reeder, of quasi-split classical groups. Finally, on the Galois side, we show that the epipelagic Langlands parameters of $G$ constructed by Reeder-Yu can be recovered via the self-duality of Bushnell-Henniart's admissible triples and endoscopic embeddings of L-groups. We also establish some related results concerning epipelagic parameters that were previously proved under restrictions on $p$, including a parity result on rectifying characters and an adjoint Swan conductor result related to the Hiraga-Ichino-Ikeda conjecture.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28189",
  "author_total": 1,
  "authors": [
    {
      "name": "Geo Kam-Fai Tam"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3wjkbrgz0jspd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28189",
  "fulltext_url": null,
  "id": "3wjkbrgz0jspd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28189",
  "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": "W7214213716",
  "pdf_url": "https://arxiv.org/pdf/2609.28189",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3wjkbrgz0jspd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.28189",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28189"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Endoscopic liftings and parameters of epipelagic representations for classical groups",
  "title_text": "Endoscopic liftings and parameters of epipelagic representations for classical groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/3wjkbrgz0jspd",
  "venue": "arXiv",
  "versions": []
}