{
  "abstract": "We present a simple combinatorial method for computing the socle of representations of $\\mathrm{GL}_n(F)$, where $F$ is a local non-Archimedean field, parabolically induced from two ladder representations satisfying a permissibility condition. We adapt recent approaches to such problems using the classical Robinson--Schensted--Knuth correspondence (RSK) and introduce a new variant of RSK that we call mixed-RSK. Some combinatorial properties of this map are investigated and then used to resolve a conjecture of Erez Lapid.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.27173",
  "author_total": 2,
  "authors": [
    {
      "name": "Ilse Fischer"
    },
    {
      "name": "Markus Reibnegger"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fzgspq4j1sbzx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.27173",
  "fulltext_url": null,
  "id": "fzgspq4j1sbzx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.27173",
  "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.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
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      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
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  ],
  "openalex": "W7204593253",
  "pdf_url": "https://arxiv.org/pdf/2608.27173",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fzgspq4j1sbzx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2608.27173",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.27173"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A Mixed Robinson--Schensted--Knuth Construction in the Representation Theory of $\\mathrm{GL}_n$ over Local non-Archimedean Fields",
  "title_text": "A Mixed Robinson--Schensted--Knuth Construction in the Representation Theory of GL_n over Local non-Archimedean Fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/fzgspq4j1sbzx",
  "venue": "arXiv",
  "versions": []
}