{
  "id": "math/0505619",
  "version": "v4",
  "published": "2005-05-30T18:47:06.000Z",
  "updated": "2024-03-14T01:26:02.000Z",
  "title": "Stabilization phenomena in Kac-Moody algebras and quiver varieties",
  "authors": [
    "Ben Webster"
  ],
  "comment": "final version, to appear in International Math Research Notices. 17 pages, 4 figures",
  "journal": "International Mathematics Research Notices, vol. 2006, Article ID 36856",
  "doi": "10.1155/IMRN/2006/36856",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let X be the Dynkin diagram of a symmetrizable Kac-Moody algebra, and X_0 a subgraph with all vertices of degree 1 or 2. Using the crystal structure on the components of quiver varieties for X, we show that if we expand X by extending X_0, the branching multiplicities and tensor product multiplicities stabilize, provided the weights involved satisfy a condition which we call ``depth'' and are supported outside $X_0$. This extends a theorem of Kleber and Viswanath. Furthermore, we show that the weight multiplicities of such representations are polynomial in the length of X_0, generalizing the same result for A_\\ell by Benkart, et al.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2006-08-29T09:27:08.000Z"
    },
    {
      "version": "v4",
      "updated": "2024-03-14T01:26:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B67"
    ],
    "keywords": [
      "quiver varieties",
      "stabilization phenomena",
      "symmetrizable kac-moody algebra",
      "weight multiplicities",
      "tensor product multiplicities stabilize"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Hindawi"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......5619W"
    }
  }
}