{
  "abstract": "Let $W$ be an irreducible complex reflection group with reflection representation $V$. A $W$-stable, faithful homogeneous system of parameters $Θ\\subseteq \\mathrm{Sym}(V^*)$ of common positive degree $p$ is called a posh hsop; $Θ$ carries a $W$-representation $U$ if $Θ\\simeq U$ as ungraded $W$-modules. We classify the posh pairs $(p,U)$ for which a posh hsop of degree $p$ carrying $U$ exists. Every such $U$ is a Galois twist of $V^*$. Extending work of Ito and Okada, we deduce that the quotient $S/(Θ)$ is a permutation module for $W$ if and only if $U \\simeq V^*$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07280",
  "author_total": 2,
  "authors": [
    {
      "name": "Jason Stack"
    },
    {
      "name": "Nathan Williams"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3as4d2bt4g360.bib",
  "cited_by": 1,
  "doi": "10.48550/arxiv.2610.07280",
  "fulltext_url": null,
  "id": "3as4d2bt4g360",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07280",
  "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.CO"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7221033122",
  "pdf_url": "https://arxiv.org/pdf/2610.07280",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3as4d2bt4g360.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.07280",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07280"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Posh Parking Spaces",
  "title_text": "Posh Parking Spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/3as4d2bt4g360",
  "venue": "arXiv",
  "versions": []
}