{
  "id": "1906.07481",
  "version": "v1",
  "published": "2019-06-18T10:22:01.000Z",
  "updated": "2019-06-18T10:22:01.000Z",
  "title": "Spinorial Representations of Symmetric Groups",
  "authors": [
    "Jyotirmoy Ganguly",
    "Steven Spallone"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "A real representation $\\pi$ of a finite group may be regarded as a homomorphism to an orthogonal group $\\Or(V)$. For symmetric groups $S_n$, alternating groups $A_n$, and products $S_n \\times S_{n'}$ of symmetric groups, we give criteria for whether $\\pi$ lifts to the double cover $\\Pin(V)$ of $\\Or(V)$, in terms of character values. From these criteria, we compute the second Stiefel-Whitney classes of these representations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-18T10:22:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symmetric groups",
      "spinorial representations",
      "second stiefel-whitney classes",
      "finite group",
      "character values"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}