{
  "id": "2208.13055",
  "version": "v1",
  "published": "2022-08-27T16:55:56.000Z",
  "updated": "2022-08-27T16:55:56.000Z",
  "title": "Howe duality and dynamical Weyl group",
  "authors": [
    "Rea Dalipi",
    "Giovanni Felder"
  ],
  "comment": "19 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We give a fermionic formula for $R$-matrices of exterior powers of the vector representations of $U_q(\\hat{\\mathfrak{gl}}_N)$ and relate it to the dynamical Weyl group of Tarasov-Varchenko and Etingof-Varchenko, via a Howe ($\\mathfrak{gl}_N,\\mathfrak{gl}_M$)-duality. As a consequence we obtain a dynamical action of the Weyl group on integrable $U_q\\mathfrak{gl}_M$-modules, extending the known action on zero weight spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-27T16:55:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B37"
    ],
    "keywords": [
      "dynamical weyl group",
      "howe duality",
      "zero weight spaces",
      "vector representations",
      "exterior powers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}