{
  "abstract": "In this paper, we compute the Möbius function on the poset of pseudo-Levi subgroups containing a fixed maximal torus of two families of finite groups, $GL_n(q)$ and $Sp_{2n}(q)$, for some natural number $n$ and a prime power $q$, where $q>2n+1$. For the general linear group, we consider arbitrary tori, but for symplectic groups, we restrict to tori corresponding to the bipartitions of $n$ into odd integers. Also, we assume $q$ is even for the case of symplectic groups. The Möbius function for the set of pseudo-Levi subgroups of a finite group $G$ is important for an explicit evaluation of the formula expressing the decomposition of tensor products of characters, as proved in Theorem 2 of the paper ''Multiplicity of characters of finite reductive groups and Drinfeld doubles'' [arXiv:2512.01432].",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.12522",
  "author_total": 1,
  "authors": [
    {
      "name": "Aritra Kundu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dq90kbtg6s5sd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.12522",
  "fulltext_url": null,
  "id": "dq90kbtg6s5sd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.12522",
  "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.CO"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7168415766",
  "pdf_url": "https://arxiv.org/pdf/2607.12522",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dq90kbtg6s5sd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2607.12522",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.12522"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Möbius functions for pseudo-Levi subgroups in finite general linear and symplectic groups",
  "title_text": "Möbius functions for pseudo-Levi subgroups in finite general linear and symplectic groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/dq90kbtg6s5sd",
  "venue": "arXiv",
  "versions": []
}