{
  "id": "1504.04685",
  "version": "v1",
  "published": "2015-04-18T05:55:54.000Z",
  "updated": "2015-04-18T05:55:54.000Z",
  "title": "On the representation theory of $G\\sim S_n$",
  "authors": [
    "Ashish Mishra",
    "Murali K. Srinivasan"
  ],
  "comment": "41 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In the Vershik-Okounkov approach to the complex irreducible representations of $S_n$ and $G\\sim S_n$ we parametrize the irreducible representations and their bases by spectral objects rather than combinatorial objects and then, at the end, give a bijection between the spectral and combinatorial objects. The fundamental ideas are similar in both cases but there are additional technicalities involved in the $G\\sim S_n$ case. This was carried out by Pushkarev. The present work gives a fully detailed exposition of Pushkarev's theory. For the most part we follow the original but our definition of a Gelfand-Tsetlin subspace, based on a multiplicity free chain of subgroups, is slightly different and leads to a more natural development of the theory. We also work out in detail an example, the generalized Johnson scheme, from this viewpoint.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-18T05:55:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "representation theory",
      "combinatorial objects",
      "multiplicity free chain",
      "vershik-okounkov approach",
      "complex irreducible representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150404685M"
    }
  }
}