{
  "id": "2006.04023",
  "version": "v1",
  "published": "2020-06-07T02:39:08.000Z",
  "updated": "2020-06-07T02:39:08.000Z",
  "title": "Local theta correspondence: the basic theory",
  "authors": [
    "Binyong Sun",
    "Chen-Bo Zhu"
  ],
  "comment": "To appear in the Proceedings of the International Congress of Chinese Mathematicians, 2018",
  "categories": [
    "math.RT"
  ],
  "abstract": "We give an elementary introduction to Classical Invariant Theory and its modern extension \"Transcending Classical Invariant Theory\", commonly known as the theory of local theta correspondence. We explain the two fundamental assertions of the theory: the Howe duality conjecture and the Kudla-Rallis conservation relation conjecture. We give a status report on the problem of explicitly describing local theta correspondence in terms of Langlands-Vogan parameters. We conclude with a discussion on a certain problem of automatic continuity, which manifests unity of the theory in algebraic and smooth settings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-07T02:39:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E46",
      "22E50"
    ],
    "keywords": [
      "local theta correspondence",
      "basic theory",
      "kudla-rallis conservation relation conjecture",
      "howe duality conjecture",
      "automatic continuity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}