{
  "abstract": "For the Iwahori-Hecke algebras $\\mathcal H_q(\\mathfrak S_n)$ of the symmetric group $\\mathfrak S_n$ at a primitive $e$-th root of unity, James and Mathas proved a theorem which relates $v$-decomposition numbers $d_{λμ}^{e}(v)$ for different values of $e$, by adding ``empty runners'' to the abacus display for the labelling partitions $λ,μ$. Fayers proved a similar theorem, which involves adding ``full'' runners to these abacus displays. In this paper we use Uglov's map from the set of $r$-abaci for $r$-partitions to the set of $e$-abaci for partitions to extend these theorems to the cyclotomic Hecke algebras of type $G(r,1,n)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15115",
  "author_total": 2,
  "authors": [
    {
      "name": "Jun Hu"
    },
    {
      "name": "Xiangyu Qi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/24h24t4n10rvv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15115",
  "fulltext_url": null,
  "id": "24h24t4n10rvv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15115",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.RA"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7213285246",
  "pdf_url": "https://arxiv.org/pdf/2609.15115",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/24h24t4n10rvv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.15115",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15115"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "New runner removal theorems for the cyclotomic Hecke algebras of type $G(r,1,n)$",
  "title_text": "New runner removal theorems for the cyclotomic Hecke algebras of type G(r,1,n)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/24h24t4n10rvv",
  "venue": "arXiv",
  "versions": []
}