{
  "abstract": "{We study the module structure of the polynomial ring, localized at the discriminant, over the ring of differential operators on the ring of invariants of the imprimitive complex reflection group $G(r,p,n)$, describing its simple components with explicit generators given by the higher Specht polynomials of Ariki--Terasoma--Yamada. The proof rests on a Jacobian lemma computing the discriminant of $G(r,p,n)$, combined with a double-centralizer argument. As particular cases ($r=2$, $p=2$ or $p=1$) we recover, and considerably shorten, the known decomposition theorems for the real reflection groups $W(D_n)$ and $W(B_n)$; we also treat $G(r,r,n)$ and $G(r,1,n)$ explicitly, with worked examples ($D_2$, $D_3$, $B_2$) and their central idempotents. Finally, applying the Galois descent equivalence of categories of Nonkané to $G(r,p,n)$ for the first time gives a second, generator-free description of the simple summands as twisted invariants.}",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.01474",
  "author_total": 2,
  "authors": [
    {
      "name": "Jean Kaboré"
    },
    {
      "name": "Ibrahim Nonkané"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dab04v48ektb2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.01474",
  "fulltext_url": null,
  "id": "dab04v48ektb2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.01474",
  "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.GR"
    ],
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      "arxiv",
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    ],
    [
      "openalex",
      "2602|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7172388940",
  "pdf_url": "https://arxiv.org/pdf/2608.01474",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dab04v48ektb2.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T06:21:33Z",
      "native_id": "2608.01474",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.01474"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A uniform decomposition theorem for invariant differential operators on imprimitive complex reflection groups G(r,p,n)",
  "title_text": "A uniform decomposition theorem for invariant differential operators on imprimitive complex reflection groups G(r,p,n)",
  "type": "preprint",
  "updated_at": "2026-11-10T06:21:33Z",
  "url": "https://research.draconitic.com/paper/dab04v48ektb2",
  "venue": "arXiv",
  "versions": []
}