{
  "abstract": "Let $G$ be a $p$-adic unipotent group and let $H$ be an algebraic subgroup of $G$. Given a unitary character $χ$ of $H$, we consider the monomial representation $\\operatorname{Ind}_{H}^{G}χ$. To the character $χ$, we associate the affine subspace $$ X_χ=f+\\mathfrak h^\\perp\\subset\\mathfrak g^*$$ where $f$ is a linear form associated with $χ$. We describe the irreducible representations occurring in the central decomposition of $\\operatorname{Ind}_{H}^{G}χ$ in terms of the coadjoint orbits in $\\mathfrak g^*$ that meet $X_χ$. We also determine the corresponding measure class on the unitary dual $\\widehat G$. Furthermore, we study the multiplicities of the irreducible representations in this decomposition. As an application, we compute the Plancherel formula for $\\operatorname{Ind}_{H}^{G}χ$ when $H$ is a normal algebraic subgroup of $G$ and the multiplicities are finite.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40099",
  "author_total": 1,
  "authors": [
    {
      "name": "Khemais Maktouf"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/83hanw1spmg7t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40099",
  "fulltext_url": null,
  "id": "83hanw1spmg7t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40099",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40099",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/83hanw1spmg7t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.40099",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40099"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Harmonic Analysis on $p$-adic Unipotent Groups",
  "title_text": "Harmonic Analysis on p-adic Unipotent Groups",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/83hanw1spmg7t",
  "venue": "arXiv",
  "versions": []
}