{
  "abstract": "Moustrou, Riener, and Verdure related the dominance order on partitions to Specht ideal and variety inclusion for $S_n$; we previously extended this to direct products of symmetric groups. Here we take a first step toward the imprimitive complex reflection group $G(r,1,n)=(\\mathbb{Z}/r\\mathbb{Z})\\wr S_n$. The correct geometric invariant of a point $x\\in K^n$ is a pair $(μ,z)$: a classical partition $μ$ on the $r$-th powers of the nonzero coordinates, together with the number $z$ of zero coordinates. We construct a $G(r,1,n)$-invariant ideal $I_{(μ,z)}$ for each such pair, and show that a dominance order on $(μ,z)$, with $z$ taking strict priority over $μ$, exactly characterizes both ideal inclusion and reverse variety inclusion. We settle a monomial criterion in three regimes, recover the classical $B_n$-Specht ideal theory at $r=2$ when $z=0$, and establish radicality of $I_{(μ,z)}$ at the two extremes of the $z=0$ level. Four computational examples, checked exhaustively for group invariance, illustrate the construction throughout.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29683",
  "author_total": 2,
  "authors": [
    {
      "name": "Ibrahim Nonkané"
    },
    {
      "name": "Joel Tossa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5tsn2d31q2thh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29683",
  "fulltext_url": null,
  "id": "5tsn2d31q2thh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29683",
  "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.AC"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.GR"
    ],
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      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7214326795",
  "pdf_url": "https://arxiv.org/pdf/2609.29683",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5tsn2d31q2thh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.29683",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29683"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Specht ideals for the imprimitive complex reflection group $G(r,1,n)$: geometric orbit types and a dominance theorem",
  "title_text": "Specht ideals for the imprimitive complex reflection group G(r,1,n): geometric orbit types and a dominance theorem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/5tsn2d31q2thh",
  "venue": "arXiv",
  "versions": []
}