{
  "abstract": "Given a Coxeter system $(W,S)$ and a subset $I\\subset S$. Let $W_I=\\langle I\\rangle$ be the standard parabolic subgroup of a Coxeter group $W$, and ${}^IW$ be the set of representatives of minimal length in the coset $W_I\\backslash W$. We construct a parabolic version of Soergel's standard filtration, and show that, given any Soergel bimodule, each subquotient of its parabolic filtration is a direct sum of grading shifts of $B_x^I\\otimes_R R_y$ with $x\\in W_I$ and $y\\in {}^IW$. By applying the character theorem of Elias and Williamson, we deduce the positivity of coefficients in the expansion of $C_w$ with respect to the hybrid basis $\\{C_xT_y:x\\in W_I,y\\in {}^IW\\}$. This generalizes Grojnowski and Haiman's result to any Coxeter group.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33490",
  "author_total": 2,
  "authors": [
    {
      "name": "Xun Xie"
    },
    {
      "name": "Qifan Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5vnfke4911d9y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33490",
  "fulltext_url": null,
  "id": "5vnfke4911d9y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33490",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7223921188",
  "pdf_url": "https://arxiv.org/pdf/2610.33490",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5vnfke4911d9y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33490",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33490"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Parabolic filtrations of Soergel bimodules",
  "title_text": "Parabolic filtrations of Soergel bimodules",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/5vnfke4911d9y",
  "venue": "arXiv",
  "versions": []
}