{
  "id": "2204.06166",
  "version": "v1",
  "published": "2022-04-13T04:31:48.000Z",
  "updated": "2022-04-13T04:31:48.000Z",
  "title": "Representation theoretic interpretation and interpolation properties of inhomogeneous spin $q$-Whittaker polynomials",
  "authors": [
    "Sergei Korotkikh"
  ],
  "comment": "46 pages",
  "categories": [
    "math.CO",
    "math-ph",
    "math.MP",
    "math.QA"
  ],
  "abstract": "We establish new properties of inhomogeneous spin $q$-Whittaker polynomials, which are symmetric polynomials generalizing $t=0$ Macdonald polynomials. We show that these polynomials are defined in terms of a vertex model, whose weights come not from an $R$-matrix, as is often the case, but from other intertwining operators of $U'_q(\\hat{\\mathfrak{sl}}_2)$-modules. Using this construction, we are able to prove a Cauchy-type identity for inhomogeneous spin $q$-Whittaker polynomials in full generality. Moreover, we are able to characterize spin $q$-Whittaker polynomials in terms of vanishing at certain points, and we find interpolation analogues of $q$-Whittaker and elementary symmetric polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-13T04:31:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "whittaker polynomials",
      "representation theoretic interpretation",
      "inhomogeneous spin",
      "interpolation properties",
      "elementary symmetric polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 46,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}