{
  "id": "1111.6044",
  "version": "v2",
  "published": "2011-11-25T16:22:51.000Z",
  "updated": "2011-11-29T21:22:49.000Z",
  "title": "Solution of a q-difference Noether problem and the quantum Gelfand-Kirillov conjecture for gl_N",
  "authors": [
    "Vyacheslav Futorny",
    "Jonas T. Hartwig"
  ],
  "categories": [
    "math.RA",
    "math.QA",
    "math.RT"
  ],
  "abstract": "It is shown that the q-difference Noether problem for all classical Weyl groups has a positive solution, simultaneously generalizing well known results on multisymmetric functions of Mattuck and Miyata in the case q=1, and q-deforming the noncommutative Noether problem for the symmetric group. It is also shown that the quantum Gelfand-Kirillov conjecture for gl_N (for a generic q) follows from the positive solution of the q-difference Noether problem for the Weyl group of type D_n. The proof is based on the theory of Galois rings developed by the first author and Ovsienko. From here we obtain a new proof of the quantum Gelfand-Kirillov conjecture for sl_N, thus recovering the result of Fauquant-Millet. Moreover, we provide an explicit description of skew fields of fractions for quantized gl_N and sl_N generalizing Alev and Dumas.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-11-29T21:22:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B37",
      "16K40",
      "16S30",
      "16S35"
    ],
    "keywords": [
      "quantum gelfand-kirillov conjecture",
      "q-difference noether problem",
      "weyl group",
      "positive solution",
      "symmetric group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.6044F"
    }
  }
}