{
  "abstract": "FINDING: The p-Kazhdan-Lusztig polynomials govern modular character formulas for reductive groups in positive characteristic, linking perverse sheaves on affine flag varieties to tilting module multiplicities. | MATH: The key object is the p-Kazhdan-Lusztig basis \\(\\{ \\underline{C}_w \\}\\) of the affine Hecke algebra over \\(\\mathbb{Z}\\), specializing at \\(v \\mapsto 1\\) with \\(p\\)-dependent coefficients. The character formula (Williamson–Riche) states: \\(\\mathrm{ch}(L(\\lambda)) = \\sum_{\\mu \\leq \\lambda} (-1)^{\\ell(\\lambda)-\\ell(\\mu)} P_{\\mu,\\lambda}^{(p)}(1) \\, \\mathrm{ch}(\\Delta(\\mu))\\), where \\(P_{\\mu,\\lambda}^{(p)}\\) are p-KL polynomials. These satisfy \\(P_{\\mu,\\lambda}^{(p)} = \\sum_{i} a_i v^i\\) with \\(a_i \\in \\mathbb{Z}_{\\geq 0}\\), and crucially \\(P_{\\mu,\\lambda}^{(p)} \\neq P_{\\mu,\\lambda}\\) (classical KL) for small \\(p\\). The affine flag variety \\(G((t))/I\\) (Iwahori) has perverse sheaves whose stalks compute these polynomials; the modular case requires \\(\\mathbb{F}_p\\)-coefficient\n\nAuthor: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com",
  "abstract_shown": true,
  "affiliations": [
    "Independent Researcher, United Kingdom"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Andrew Stewart Caldin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fx1wsnemz0qh0.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23635194",
  "fulltext_url": null,
  "id": "fx1wsnemz0qh0",
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  "landing_url": "https://zenodo.org/records/23635194",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
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  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fx1wsnemz0qh0.ris",
  "sources": [
    {
      "first_seen": "2026-11-08T12:21:58Z",
      "native_id": "23635194",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23635194"
    }
  ],
  "subjects": [],
  "title": "p-Kazhdan-Lusztig Polynomials Unify Modular Characters and Tilting Multiplicities — E8 Intelligence Research",
  "title_text": "p-Kazhdan-Lusztig Polynomials Unify Modular Characters and Tilting Multiplicities — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-08T12:21:58Z",
  "url": "https://research.draconitic.com/paper/fx1wsnemz0qh0",
  "venue": "Zenodo",
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}