{
  "id": "2412.20757",
  "version": "v1",
  "published": "2024-12-30T07:02:06.000Z",
  "updated": "2024-12-30T07:02:06.000Z",
  "title": "Lusztig $q$-weight multiplicities and Kirillov-Reshetikhin crystals",
  "authors": [
    "Hyeonjae Choi",
    "Donghyun Kim",
    "Seung Jin Lee"
  ],
  "comment": "60 pages, comments are welcome",
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "Lusztig $q$-weight multiplicities extend the Kostka-Foulkes polynomials to a broader range of Lie types. In this work, we investigate these multiplicities through the framework of Kirillov-Reshetikhin crystals. Specifically, for type $C$ with dominant weights and type $B$ with dominant spin weights, we present a combinatorial formula for Lusztig $q$-weight multiplicities in terms of energy functions of Kirillov-Reshetikhin crystals, generalizing the charge statistic on semistandard Young tableaux for type $A$. Additionally, we introduce level-restricted $q$-weight multiplicities for nonexceptional types, and prove positivity by providing their combinatorial formulas.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-12-30T07:02:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kirillov-reshetikhin crystals",
      "combinatorial formula",
      "semistandard young tableaux",
      "dominant spin weights",
      "weight multiplicities extend"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 60,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}