{
  "annotation_id": "9476be49-1733-4d95-a70e-1a737d234df4",
  "date_created": "2026-02-17T05:53:11.672000Z",
  "date_modified": "2026-02-17T05:53:11.672000Z",
  "file_hash": "21b9f127d4b8fea4d55ae3398163f00f274441b495427da1d5faa9d0c6af290f",
  "private": false,
  "record": {
    "abstract": "We prove the combinatorial invariance of the coefficient of $q$ in Kazhdan-Lusztig polynomials for arbitrary Coxeter groups. As a result, we obtain the Combinatorial Invariance Conjecture for Bruhat intervals of length at most $6$. We also prove the Gabber-Joseph conjecture for the second-highest $\\mathrm{Ext}$ group of a pair of Verma modules, as well as the combinatorial invariance of the dimension of this group.",
    "arxiv_id": "2601.07793",
    "authors": [
      "Grant T. Barkley",
      "Christian Gaetz",
      "Thomas Lam"
    ],
    "categories": [
      "math.CO",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Combinatorial invariance for the coefficient of $q$ in Kazhdan-Lusztig polynomials",
    "url": "https://arxiv.org/abs/2601.07793",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5942118a-c4bf-40b2-a4fe-88e698637eac",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}