{
  "id": "2204.04994",
  "version": "v1",
  "published": "2022-04-11T10:23:08.000Z",
  "updated": "2022-04-11T10:23:08.000Z",
  "title": "Arthur's Conjectures and the Orbit Method for Real Reductive Groups",
  "authors": [
    "Lucas Mason-Brown"
  ],
  "comment": "Article prepared for the Proceedings of the IHES 2022 summer school on the Langlands program. Comments welcome!",
  "categories": [
    "math.RT"
  ],
  "abstract": "The first half of this article is expository -- I will review, with examples, the main statements of the Langlands classification and Arthur's conjectures for real reductive groups as formulated by Adams, Barbasch, and Vogan. In the second half, I will turn my attention to the Orbit Method, a conjectural scheme for classifying irreducible unitary representations of a real reductive group. I will give a definition of the Orbit Method in the case when the group is complex. The main input is the theory of unipotent ideals and Harish-Chandra bimodules, developed in arXiv:2108.03453. I will show that the Orbit Method I define is related to Arthur's conjectures via a natural duality map. Finally, I will sketch a possible generalization of this Orbit Method for arbitrary real groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-11T10:23:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E46"
    ],
    "keywords": [
      "real reductive group",
      "orbit method",
      "arthurs conjectures",
      "natural duality map",
      "arbitrary real groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}