{
  "abstract": "We record two results on additive diameters of group representations. First we give a corrected version of Proposition 5.3 from the first arXiv version of arXiv:2504.07573. Let $0<\\varepsilon<1/3$, let $n>9/\\varepsilon^2$, and let $U\\leq\\mathfrak{sl}_n(\\mathbb{C})$ with $\\dim U>\\varepsilon n^2$. Then $\\operatorname{diam}^{\\mathrm{SL}_n(\\mathbb{C})}_{+}(\\mathfrak{sl}_n(\\mathbb{C}),U)\\leq 32/\\varepsilon+8$. The proof uses an averaging argument for the action of the symmetric group on the off-diagonal matrix positions. This argument was subsequently developed further in arXiv:2609.03882. We also prove the right-hand inequality in Question 6.7 of arXiv:2504.07573. If $G$ is a complex algebraic group, $V$ is a finite-dimensional $G$-module, $U\\leq V$, and $\\mathfrak g=\\operatorname{Lie}(G)$, then $\\operatorname{diam}^{G}_{+}(V,U)\\leq\\operatorname{diam}^{\\mathfrak g}_{+}(V,U)$. No irreducibility or connectedness assumption is needed.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06023",
  "author_total": 1,
  "authors": [
    {
      "name": "Ernesto Ingrosso"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/16eha7qqde7zb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06023",
  "fulltext_url": null,
  "id": "16eha7qqde7zb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06023",
  "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.GR"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7212024540",
  "pdf_url": "https://arxiv.org/pdf/2609.06023",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/16eha7qqde7zb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06023",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06023"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A Note on Additive Diameter",
  "title_text": "A Note on Additive Diameter",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/16eha7qqde7zb",
  "venue": "arXiv",
  "versions": []
}