{
  "abstract": "Let $p$ be an odd prime, and let $ρ\\colon G\\to \\GSp_{2n}(\\Z_p)$ be an irreducible symplectic residually multiplicity free representation. We define the symplectic extension graph $Γ_ρ^\\GSp$ associated with $ρ$ to be the directed graph whose vertices are the residual factors of $ρ$ and a directed edge between two vertices corresponds to a nonsplit extension between the vertices realized by $ρ$. Using the Euclidean Bruhat--Tits building associated with $\\GSp_{2n}(\\Q_p)$, under some assumptions, we prove the existence of certain paths in $Γ_ρ^\\GSp$ and show that $Γ_ρ^\\GSp$ is a disjoint union of nonempty strongly connected subgraphs. Moreover, we provide examples to show that the result we obtain is optimal.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19434",
  "author_total": 1,
  "authors": [
    {
      "name": "Aniruddha Sudarshan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dgwp1r6pasede.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19434",
  "fulltext_url": null,
  "id": "dgwp1r6pasede",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19434",
  "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.NT"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7222195669",
  "pdf_url": "https://arxiv.org/pdf/2610.19434",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dgwp1r6pasede.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19434",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19434"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Symplectic extension graphs and Ribet's lemma",
  "title_text": "Symplectic extension graphs and Ribet's lemma",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/dgwp1r6pasede",
  "venue": "arXiv",
  "versions": []
}