{
  "id": "1401.6321",
  "version": "v3",
  "published": "2014-01-24T12:01:31.000Z",
  "updated": "2014-03-04T15:39:01.000Z",
  "title": "Representation theory in complex rank, I",
  "authors": [
    "Pavel Etingof"
  ],
  "comment": "26 pages, latex",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "P. Deligne defined interpolations of the tensor category of representations of the symmetric group S_n to complex values of n. Namely, he defined tensor categories Rep(S_t) for any complex t. This construction was generalized by F. Knop to the case of wreath products of S_n with a finite group. Generalizing these results, we propose a method of interpolating representations categories of various algebras containing S_n (such as degenerate affine Hecke algebras, symplectic reflection algebras, rational Cherednik algebras, etc.) to complex values of n. We also define the group algebra of S_n for complex n, study its properties, and propose a Schur-Weyl duality for Rep(S_t). In version 2, same more details have been added.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-03-04T15:39:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "representation theory",
      "complex rank",
      "tensor category",
      "degenerate affine hecke algebras",
      "complex values"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.6321E"
    }
  }
}