{
  "id": "1407.2706",
  "version": "v1",
  "published": "2014-07-10T06:30:24.000Z",
  "updated": "2014-07-10T06:30:24.000Z",
  "title": "SUSY structures, representations and Peter-Weyl theorem for $S^{1|1}$",
  "authors": [
    "C. Carmeli",
    "R. Fioresi",
    "S. D. Kwok"
  ],
  "categories": [
    "math.RT",
    "math-ph",
    "math.MP",
    "math.RA"
  ],
  "abstract": "The real compact supergroup $S^{1|1}$ is analized from different perspectives and its representation theory is studied. We prove it is the only (up to isomorphism) supergroup, which is a real form of $({\\mathbf C}^{1|1})^\\times$ with reduced Lie group $S^1$, and a link with SUSY structures on ${\\mathbf C}^{1|1}$ is established. We describe a large family of complex semisimple representations of $S^{1|1}$ and we show that any $S^{1|1}$-representation whose weights are all nonzero is a direct sum of members of our family. We also compute the matrix elements of the members of this family and we give a proof of the Peter-Weyl theorem for $S^{1|1}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-10T06:30:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "peter-weyl theorem",
      "susy structures",
      "real compact supergroup",
      "complex semisimple representations",
      "real form"
    ],
    "publication": {
      "doi": "10.1016/j.geomphys.2015.05.005",
      "journal": "Journal of Geometry and Physics",
      "year": 2015,
      "month": "Sep",
      "volume": 95,
      "pages": 144
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1305719,
      "adsabs": "2015JGP....95..144C"
    }
  }
}