{
  "id": "2207.02459",
  "version": "v1",
  "published": "2022-07-06T06:06:03.000Z",
  "updated": "2022-07-06T06:06:03.000Z",
  "title": "Evaluation birepresentations of affine type A Soergel bimodules",
  "authors": [
    "M. Mackaay",
    "V. Miemietz",
    "P. Vaz"
  ],
  "comment": "61 pages, lots of colored pictures",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "In this paper, we use Soergel calculus to define a monoidal functor, called the evaluation functor, from extended affine type A Soergel bimodules to the homotopy category of bounded complexes in finite type A Soergel bimodules. This functor categorifies the well-known evaluation homomorphism from the extended affine type A Hecke algebra to the finite type A Hecke algebra. Through it, one can pull back the triangulated birepresentation induced by any finitary birepresentation of finite type A Soergel bimodules to obtain a triangulated birepresentation of extended affine type A Soergel bimodules. We show that if the initial finitary birepresentation in finite type A is a cell birepresentation, the evaluation birepresentation in extended affine type A has a finitary cover, which we illustrate by working out the case of cell birepresentations with subregular apex in detail.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-06T06:06:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "soergel bimodules",
      "extended affine type",
      "evaluation birepresentation",
      "finite type",
      "cell birepresentation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 61,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}