{
  "id": "2309.01287",
  "version": "v1",
  "published": "2023-09-03T23:04:19.000Z",
  "updated": "2023-09-03T23:04:19.000Z",
  "title": "Integral expressions for derivations of multiarrangements",
  "authors": [
    "Misha Feigin",
    "Zixuan Wang",
    "Masahiko Yoshinaga"
  ],
  "comment": "21 pages",
  "categories": [
    "math.CO",
    "math.AC",
    "math.RT"
  ],
  "abstract": "The construction of an explicit basis for a free multiarrangement is not easy in general. Inspired by the integral expressions for quasi-invariants of quantum Calogero-Moser systems, we present integral expressions for specific bases of certain multiarrangements. Our construction covers the cases of three lines in dimension $2$ (previously examined by Wakamiko) and free multiarrangements associated with complex reflection groups (Hoge, Mano, R\\\"ohrle, Stump). Furthermore, we propose a conjectural basis for the module of logarithmic vector fields of the extended Catalan arrangement of type $B_2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-03T23:04:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32S22",
      "52C35",
      "13N15",
      "20F55"
    ],
    "keywords": [
      "integral expressions",
      "derivations",
      "free multiarrangement",
      "quantum calogero-moser systems",
      "complex reflection groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}