{
  "id": "2502.02841",
  "version": "v1",
  "published": "2025-02-05T02:57:15.000Z",
  "updated": "2025-02-05T02:57:15.000Z",
  "title": "On the Boson-Fermion Correspondence for Factorial Schur Functions",
  "authors": [
    "Daniel Bump",
    "Andrew Hardt",
    "Travis Scrimshaw"
  ],
  "comment": "26 pages",
  "categories": [
    "math.CO",
    "math-ph",
    "math.MP",
    "math.RT"
  ],
  "abstract": "We give an algebraic (non-analytic) proof of the deformed boson-fermion Fock space construction of Molev's double supersymmetric Schur functions, among other results, from our previous paper. In other words, we make no assumptions on the variables and parameters. By specializing to a finite number of variables and shifting parameters, we recover the factorial Schur functions. Furthermore, we realize the bosonic construction through a representation of a completion of the infinite rank general linear Lie algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-02-05T02:57:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "factorial schur functions",
      "boson-fermion correspondence",
      "double supersymmetric schur functions",
      "infinite rank general linear lie",
      "rank general linear lie algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}