{
  "id": "1910.02538",
  "version": "v1",
  "published": "2019-10-06T21:50:10.000Z",
  "updated": "2019-10-06T21:50:10.000Z",
  "title": "Upper Triangularity for Unipotent Representations",
  "authors": [
    "Lucas Mason-Brown"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Suppose $G$ is a real reductive group. The determination of the irreducible unitary representations of $G$ is one of the major unsolved problem in representation theory. There is evidence to suggest that every irreducible unitary representation of $G$ can be constructed through a sequence of well-understood operations from a finite set of building blocks, called the unipotent representations. These representations are `attached' (in a certain mysterious sense) to the nilpotent orbits of $G$ on the dual space of its Lie algebra. Inside this finite set is a still smaller set, consisting of the unipotent representations attached to non-induced nilpotent orbits. In this paper, we prove that in many cases this smaller set generates (through a suitable kind of induction) all unipotent representations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-06T21:50:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E47"
    ],
    "keywords": [
      "unipotent representations",
      "upper triangularity",
      "irreducible unitary representation",
      "finite set",
      "smaller set generates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}