{
  "abstract": "We study morphisms from symmetric powers of exterior powers to determinant-twisted endomorphism representations of general linear groups. At the minimal positive determinant twist, we prove vanishing over every field of characteristic different from two: if the exterior degree r >= 3 is odd, the symmetric degree satisfies d >= 3, and the underlying space has dimension rd, then the corresponding equivariant Hom space is zero. The proof uses a block-exchange sign and a universal root-subgroup identity, so it also applies in small odd characteristics without semisimplicity. We then determine the second-twist spaces for trivectors in characteristic zero. In dimension 3m and degree 2m, they are scalar and one-dimensional for m = 2, and zero for m >= 3. Plethystic conjugation reduces the latter vanishing to an elementary weight-support bound for exterior powers of the ten-dimensional space of ternary cubics. Finally, over fields of characteristic zero or odd characteristic, an exact computer-assisted classification in dimension nine gives a one-dimensional scalar Hom space in characteristic five and zero in characteristic zero and in every odd characteristic other than five.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25029",
  "author_total": 1,
  "authors": [
    {
      "name": "Jingchuan Ma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1yncpmmbgsv9z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25029",
  "fulltext_url": null,
  "id": "1yncpmmbgsv9z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25029",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7214079527",
  "pdf_url": "https://arxiv.org/pdf/2609.25029",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1yncpmmbgsv9z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.25029",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25029"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Low-Twist Matrix Covariants of Exterior Powers: Vanishing and Modular Phenomena",
  "title_text": "Low-Twist Matrix Covariants of Exterior Powers: Vanishing and Modular Phenomena",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/1yncpmmbgsv9z",
  "venue": "arXiv",
  "versions": []
}