{
  "id": "1309.5216",
  "version": "v2",
  "published": "2013-09-20T09:22:55.000Z",
  "updated": "2013-11-05T07:33:15.000Z",
  "title": "The A_{2n}^{(2)} Rogers-Ramanujan identities",
  "authors": [
    "S. Ole Warnaar"
  ],
  "comment": "26 pages. Two new theorems have been added to the paper (Theorems 1.5 and 4.1), giving new Rogers-Ramanujan identities for the affine Lie algebra A_{n-1}^{(1)}",
  "categories": [
    "math.CO",
    "math.NT",
    "math.RT"
  ],
  "abstract": "The famous Rogers-Ramanujan and Andrews--Gordon identities are embedded in a doubly-infinite family of Rogers-Ramanujan-type identities labelled by positive integers m and n. For fixed m and n the product side corresponds to a specialised character of the affine Kac-Moody algebra A_{2n}^{(2)} at level m, and is expressed as a product of n^2 theta functions of modulus 2m+2n+1, or by level-rank duality, as a product of m^2 theta functions. Rogers-Ramanujan-type identities for even moduli, corresponding to the affine Lie algebras C_n^{(1)} and D_{n+1}^{(2)}, are also proven.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-11-05T07:33:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05",
      "05E10",
      "11P84",
      "17B67",
      "33D67"
    ],
    "keywords": [
      "rogers-ramanujan identities",
      "rogers-ramanujan-type identities",
      "theta functions",
      "product side corresponds",
      "affine kac-moody algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.5216W"
    }
  }
}