{
  "id": "1908.04707",
  "version": "v1",
  "published": "2019-08-13T15:45:54.000Z",
  "updated": "2019-08-13T15:45:54.000Z",
  "title": "Two-row $W$-graphs in affine type $A$",
  "authors": [
    "Dongkwan Kim",
    "Pavlo Pylyavskyy"
  ],
  "comment": "comments welcome!",
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "For affine symmetric groups we construct finite $W$-graphs corresponding to two-row shapes, and prove their uniqueness. This gives the first non-trivial family of examples of finite $W$-graphs in an affine type. We compare our construction with quotients of periodic $W$-graphs defined by Lusztig. Under certain positivity assumption on the latter the two are shown to be isomorphic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-13T15:45:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "affine type",
      "affine symmetric groups",
      "construct finite",
      "two-row shapes",
      "positivity assumption"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}