{
  "abstract": "In this paper we obtain a complete description of all indecomposable characters (central positive-definite functions) of \"block-diagonal\" inductive limits of semidirect products $\\mathbb{T}^N\\rtimes\\mathfrak{S}_{N}$ of the compact $N$-dimensional torus $\\mathbb{T}^{N}$ with the symmetric group $\\mathfrak{S}_{N}$. The classification is proved by means of a variant of the ergodic method of Vershik and Kerov, namely by studying the weak limits of characters of finite-dimensional subgroups. As an application of our results, we give another proof of the classification of indecomposable characters of the infinite unitary group with block diagonal embeddings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25275",
  "author_total": 2,
  "authors": [
    {
      "name": "Nikolay Nessonov"
    },
    {
      "name": "Nhok Tkhai Shon Ngo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9sd6q77v17y58.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25275",
  "fulltext_url": null,
  "id": "9sd6q77v17y58",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25275",
  "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.OA"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7214096035",
  "pdf_url": "https://arxiv.org/pdf/2609.25275",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9sd6q77v17y58.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.25275",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25275"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Indecomposable characters of the wreath product of a torus by the infinite block-diagonal symmetric group",
  "title_text": "Indecomposable characters of the wreath product of a torus by the infinite block-diagonal symmetric group",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/9sd6q77v17y58",
  "venue": "arXiv",
  "versions": []
}