{
  "abstract": "We introduce two new monomial bases for the top $t$-degree component of the Garsia-Haiman module $V_μ$ for every partition $μ$. Both bases are indexed by column-strict standard fillings of shape $μ$; the first has exponents governed by entrywise refinements of Haglund's combinatorial statistics for the modified Macdonald polynomials $\\widetilde{H}_μ(X;q,t)$. The second basis has exponents governed by an insertion algorithm of Bhattacharya-Ratheesh-Viswanath, and gives a basis realization of the ``fermionic formula\" of the $m_{1^n}$-coefficient of the $q$-Whittaker polynomial. Our proof uses orbit harmonics, and is inspired by the original approach of Garsia and Haiman.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39061",
  "author_total": 1,
  "authors": [
    {
      "name": "Raymond Chou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c1yct6t0xyd0t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39061",
  "fulltext_url": null,
  "id": "c1yct6t0xyd0t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39061",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39061",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c1yct6t0xyd0t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39061",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39061"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Bases for the Top-Degree Garsia-Haiman Module",
  "title_text": "Bases for the Top-Degree Garsia-Haiman Module",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/c1yct6t0xyd0t",
  "venue": "arXiv",
  "versions": []
}