{
  "id": "2112.12405",
  "version": "v2",
  "published": "2021-12-23T07:56:44.000Z",
  "updated": "2022-01-12T16:04:05.000Z",
  "title": "Automorphisms and symplectic leaves of Calogero-Moser spaces",
  "authors": [
    "Cédric Bonnafé"
  ],
  "comment": "30 pages",
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "We study the symplectic leaves of the subvariety of fixed points of an automorphism of a Calogero-Moser space induced by an element of finite order of the normalizer of the associated complex reflection group $W$. We give a parametrization {\\it \\`a la Harish-Chandra} of its symplectic leaves (generalizing earlier works of Bellamy and Losev). This result is inspired by the mysterious relations between the geometry of Calogero-Moser spaces and unipotent representations of finite reductive groups, which will be the theme of a forthcoming paper.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-01-12T16:04:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "calogero-moser space",
      "symplectic leaves",
      "automorphism",
      "associated complex reflection group",
      "finite reductive groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}