{
  "abstract": "Let $\\mathbb{F}_q$ be a finite field of any characteristic and $\\rm GL(n,\\mathbb{F}_q)$ the general linear group over $\\mathbb{F}_q$. Suppose $W$ denotes the standard representation of $\\rm GL(n,\\mathbb{F}_q)$ and $\\rm GL(n,\\mathbb{F}_q)$ acts diagonally on the direct sum of $W$ and its dual space $W^*$. Let $G$ be any subgroup of $\\rm GL(n,\\mathbb{F}_q)$. Suppose the invariant field $\\mathbb{F}_q(W)^G=\\mathbb{F}_q(f_1,f_2,\\dots,f_k)$, where $f_1,f_2,\\dots,f_k\\in\\mathbb{F}_q[W]^G$ are homogeneous invariant polynomials. We prove that there exist homogeneous polynomials $\\ell_1,\\ell_2,\\dots,\\ell_{n}$ in the invariant ring $\\mathbb{F}_q[W\\oplus W^*]^{G}$ such that the invariant field $\\mathbb{F}_q(W\\oplus W^*)^{G}$ is generated by $\\{f_1,f_2,\\dots,f_k,\\ell_1,\\ell_2,\\dots,\\ell_{n}\\}$ over $\\mathbb{F}_q$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Algebra Colloquium 27:4 (2020) 749--752",
  "arxiv": "2610.15442",
  "author_total": 2,
  "authors": [
    {
      "name": "Ying Han"
    },
    {
      "name": "Runxuan Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/20jgg0zntwmbh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15442",
  "fulltext_url": null,
  "id": "20jgg0zntwmbh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15442",
  "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.AC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.15442",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/20jgg0zntwmbh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15442",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15442"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On modular vector invariant fields",
  "title_text": "On modular vector invariant fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/20jgg0zntwmbh",
  "venue": "arXiv",
  "versions": []
}