{
  "id": "2112.13684",
  "version": "v2",
  "published": "2021-12-23T07:55:32.000Z",
  "updated": "2022-01-12T06:14:12.000Z",
  "title": "Calogero-Moser spaces vs unipotent representations",
  "authors": [
    "Cédric Bonnafé"
  ],
  "comment": "52 pages",
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "Lusztig's classification of unipotent representations of finite reductive groups depends only on the associated Weyl group $W$ (endowed with its Frobenius automorphism). All the structural questions (families, Harish-Chandra series, partition into blocks...) have an answer in a combinatorics that can be entirely built directly from $W$. Over the years, we have noticed that the same combinatorics seems to be encoded in the Poisson geometry of a Calogero-Moser space associated with $W$ (roughly speaking, families correspond to ${\\mathbb{C}}^\\times$-fixed points, Harish-Chandra series correspond to symplectic leaves, blocks correspond to symplectic leaves in the fixed point subvariety under the action of a root of unity). The aim of this survey is to gather all these observations, state precise conjectures and provide general facts and examples supporting these conjectures.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-01-12T06:14:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "calogero-moser space",
      "unipotent representations",
      "symplectic leaves",
      "harish-chandra series correspond",
      "fixed point"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 52,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}