{
  "id": "1403.7320",
  "version": "v1",
  "published": "2014-03-28T10:01:12.000Z",
  "updated": "2014-03-28T10:01:12.000Z",
  "title": "Projective Oscillator Representations of sl(n+1) and sp(2m+2)",
  "authors": [
    "Xiaoping Xu"
  ],
  "comment": "15pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "The n-dimensional projective group gives rise to a one-parameter family of inhomogeneous first-order differential operator representations of sl(n+1). By partially swapping differential operators and multiplication operators, we obtain more general differential operator representations of sl(n+1). Letting these differential operators act on the corresponding polynomial algebra and the space of exponential-polynomial functions, we construct new multi-parameter families of explicit infinite-dimensional irreducible representations for s(n+1) and sp(2m+2) when n=2m+1. Our results can be viewed as extensions of Howe's oscillator construction of infinite-dimensional multiplicity-free irreducible representations for sl(n).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-28T10:01:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10"
    ],
    "keywords": [
      "projective oscillator representations",
      "inhomogeneous first-order differential operator representations",
      "general differential operator representations",
      "differential operators act",
      "explicit infinite-dimensional irreducible representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.7320X"
    }
  }
}