{
  "id": "1603.09673",
  "version": "v1",
  "published": "2016-03-31T16:31:36.000Z",
  "updated": "2016-03-31T16:31:36.000Z",
  "title": "Parity preservation for $K$-types in an irreducible representation",
  "authors": [
    "Xiang Fan"
  ],
  "comment": "7 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "A phenomenon of parity preservation for $K$-types occurring in an irreducible admissible representation happens for various reductive Lie groups. This note gives a uniform proof of this fact for members of real reductive dual pairs, by applying Howe's duality theory of theta correspondence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-31T16:31:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E46",
      "11F27"
    ],
    "keywords": [
      "parity preservation",
      "irreducible representation",
      "real reductive dual pairs",
      "applying howes duality theory",
      "theta correspondence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160309673F"
    }
  }
}