{
  "id": "1212.5771",
  "version": "v1",
  "published": "2012-12-23T08:12:09.000Z",
  "updated": "2012-12-23T08:12:09.000Z",
  "title": "Assembling crystals of type A",
  "authors": [
    "Vladimir I. Danilov",
    "Alexander V. Karzanov",
    "Gleb A. Koshevoy"
  ],
  "comment": "24 pages. This is an improved version of the first part of ArXiv:1201.4549v3[math.CO]",
  "categories": [
    "math.CO"
  ],
  "abstract": "Regular $A_n$-crystals are certain edge-colored directed graphs which are related to representations of the quantized universal enveloping algebra $U_q(\\mathfrak{sl}_{n+1})$. For such a crystal $K$ with colors $1,2,...,n$, we consider its maximal connected subcrystals with colors $1,...,n-1$ and with colors $2,...,n$ and characterize the interlacing structure for all pairs of these subcrystals. This is used to give a recursive description of the combinatorial structure of $K$ and develop an efficient procedure of assembling $K$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-12-23T08:12:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B37",
      "05C75",
      "05E99"
    ],
    "keywords": [
      "assembling crystals",
      "maximal connected subcrystals",
      "quantized universal enveloping algebra",
      "combinatorial structure",
      "efficient procedure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.5771D"
    }
  }
}