{
  "id": "2502.00478",
  "version": "v1",
  "published": "2025-02-01T16:05:50.000Z",
  "updated": "2025-02-01T16:05:50.000Z",
  "title": "Orthogonality of spin $q$-Whittaker polynomials",
  "authors": [
    "Matteo Mucciconi"
  ],
  "comment": "Comments are welcome",
  "categories": [
    "math.CO",
    "math-ph",
    "math.MP",
    "math.RT"
  ],
  "abstract": "The inhomogeneous spin $q$-Whittaker polynomials are a family of symmetric polynomials which generalize the Macdonald polynomials at $t=0$. In this paper we prove that they are orthogonal with respect to a variant of the Sklyanin measure on the $n$ dimensional torus and as a result they form a basis of the space of symmetric polynomials in $n$ variables. Instrumental to the proof are inhomogeneous eigenrelations, which partially generalize those of Macdonald polynomials. We also consider several special cases of the inhomogeneous spin $q$-Whittaker polynomials, which include variants of symmetric Grothendieck polynomials or spin Whittaker functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-02-01T16:05:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05",
      "33C47",
      "33D52"
    ],
    "keywords": [
      "whittaker polynomials",
      "symmetric polynomials",
      "orthogonality",
      "macdonald polynomials",
      "inhomogeneous spin"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}