{
  "id": "2009.13786",
  "version": "v1",
  "published": "2020-09-29T05:31:39.000Z",
  "updated": "2020-09-29T05:31:39.000Z",
  "title": "Web Calculus and Tilting Modules in Type $C_2$",
  "authors": [
    "Elijah Bodish"
  ],
  "comment": "33 pages, many figures, preliminary version",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "Using Kuperberg's $B_2/C_2$ webs, and following Elias and Libedinsky, we describe a \"light leaves\" algorithm to construct a basis of morphisms between arbitrary tensor products of fundamental representations for $\\mathfrak{so}_5\\cong \\mathfrak{sp}_4$ (and the associated quantum group). Our argument has very little dependence on the base field. As a result, we prove that when $[2]_q\\ne 0$, the Karoubi envelope of the $C_2$ web category is equivalent to the category of tilting modules for the divided powers quantum group $\\mathcal{U}_q^{\\mathbb{Z}}(\\mathfrak{sp}_4)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-29T05:31:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "tilting modules",
      "web calculus",
      "divided powers quantum group",
      "arbitrary tensor products",
      "little dependence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}