{
  "id": "1901.07616",
  "version": "v1",
  "published": "2019-01-22T21:20:28.000Z",
  "updated": "2019-01-22T21:20:28.000Z",
  "title": "Conic Representations of Topological Groups",
  "authors": [
    "Matan Tal"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We define basic notions in the category of conic representations of a topological group and prove elementary facts about them. We show that a conic representation determines an ordinary dynamical system of the group together with a multiplier, establishing facts and formulae connecting the two categories. The topic is also closely related to the affine representations of the group. The central goal was attaining a better understanding of irreducible conic representations of a group, and - particularly - to determine whether there is a phenomenon analogous to the existence of a universal irreducible affine representation of a group in our category (the general answer is negative). Then we inspect embeddings of irreducible conic representations of semi-simple Lie groups in some \"regular\" conic representation they possess. We conclude with what is known to us about the irreducible conic representations of $SL_{2}\\left(\\mathbb{R}\\right)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-22T21:20:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "topological group",
      "irreducible conic representations",
      "semi-simple lie groups",
      "universal irreducible affine representation",
      "define basic notions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}