{
  "abstract": "This paper presents a comprehensive study of the characteristic polynomial of matrix tuples and finite dimensional group representations. Among other things, several key concepts are introduced, including the minimal polynomial, algebraic extension, spectral index and multiplicity, and characteristic graph. Notably, this framework leads to a complete resolution of Kippenhahn's conjecture by providing necessary and sufficient conditions for its validity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.14194",
  "author_total": 2,
  "authors": [
    {
      "name": "Michael Stessin"
    },
    {
      "name": "Rongwei Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ckfyfrmw647x2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.14194",
  "fulltext_url": null,
  "id": "ckfyfrmw647x2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.14194",
  "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.RT"
    ],
    [
      "arxiv",
      "math.SP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2608.14194",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ckfyfrmw647x2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2608.14194",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.14194"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Reducibility of linear representations, free ideals, and Kippenhahn's conjecture",
  "title_text": "Reducibility of linear representations, free ideals, and Kippenhahn's conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/ckfyfrmw647x2",
  "venue": "arXiv",
  "versions": []
}