{
  "abstract": "We discuss dominant representations (or Young diagrams), in thermal matrix models with gauge symmetry from the perspective of partial deconfinement. We propose a prescription for defining the dominant representations for thermal matrix models with interaction terms. As an explicit example, we consider the large-$N$ Gaussian matrix model. We obtain the Vershik--Kerov--Logan--Shepp (VKLS) shape of the dominant Young diagrams through a new analytic saddle-point analysis based on a mapping of the representation theory of U($\\infty$) to free fermions in two spacetime dimensions. This computation provides a direct derivation of the previously observed functional relation between the shape of the dominant Young diagrams and the eigenvalue distribution of the thermal holonomy: the position of the complex saddle point is naturally identified with the eigenvalue. The dominant Young diagrams admit a natural interpretation in terms of partial deconfinement: the number of rows in the dominant Young diagrams matches the size of the submatrix corresponding to the deconfined subsector.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13067",
  "author_total": 2,
  "authors": [
    {
      "name": "Hidehiko Shimada"
    },
    {
      "name": "Hiromasa Watanabe"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8925g76a3kxsc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13067",
  "fulltext_url": null,
  "id": "8925g76a3kxsc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13067",
  "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",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2613|Random Matrices and Applications"
    ]
  ],
  "openalex": "W7213044143",
  "pdf_url": "https://arxiv.org/pdf/2609.13067",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8925g76a3kxsc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2609.13067",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13067"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Dominant Young Diagrams in Matrix Models and Partial Deconfinement",
  "title_text": "Dominant Young Diagrams in Matrix Models and Partial Deconfinement",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/8925g76a3kxsc",
  "venue": "arXiv",
  "versions": []
}