{
  "id": "2202.03213",
  "version": "v1",
  "published": "2022-02-07T14:17:24.000Z",
  "updated": "2022-02-07T14:17:24.000Z",
  "title": "Quantum KdV hierarchy and quasimodular forms",
  "authors": [
    "Jan-Willem M. van Ittersum",
    "Giulio Ruzza"
  ],
  "comment": "19 pages",
  "categories": [
    "math-ph",
    "math.AG",
    "math.MP",
    "math.NT"
  ],
  "abstract": "Dubrovin has shown that the spectrum of the quantization (with respect to the first Poisson structure) of the dispersionless Korteweg--de Vries (KdV) hierarchy is given by shifted symmetric functions; the latter are related by the Bloch--Okounkov Theorem to quasimodular forms on the full modular group. We extend the relation to quasimodular forms to the full quantum KdV hierarchy (and to the more general Intermediate Long Wave hierarchy). These quantum integrable hierarchies have been described by Buryak and Rossi in terms of the Double Ramification cycle in the moduli space of curves. The main tool and conceptual contribution of the paper is a general effective criterion for quasimodularity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-07T14:17:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quasimodular forms",
      "general intermediate long wave hierarchy",
      "full quantum kdv hierarchy",
      "first poisson structure",
      "full modular group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}