{
  "id": "2311.03905",
  "version": "v1",
  "published": "2023-11-07T11:40:16.000Z",
  "updated": "2023-11-07T11:40:16.000Z",
  "title": "Young wall realizations of level 1 irreducible highest weight and Fock space crystals of quantum affine algebras in type E",
  "authors": [
    "Duncan Laurie"
  ],
  "comment": "50 pages, comments very welcome",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "We construct Young wall models for the crystal bases of level $1$ irreducible highest weight representations and Fock space representations of quantum affine algebras in types $E_{6}^{(1)}$, $E_{7}^{(1)}$ and $E_{8}^{(1)}$. In each case, Young walls consist of coloured blocks stacked inside the relevant Young wall pattern which satisfy a certain combinatorial condition. Moreover the crystal structure is described entirely in terms of adding and removing blocks.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-07T11:40:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E10",
      "17B37",
      "20G42"
    ],
    "keywords": [
      "quantum affine algebras",
      "irreducible highest weight",
      "fock space crystals",
      "young wall realizations",
      "construct young wall models"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 50,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}