{
  "id": "1704.00089",
  "version": "v1",
  "published": "2017-04-01T00:38:14.000Z",
  "updated": "2017-04-01T00:38:14.000Z",
  "title": "Character Formulas from Matrix Factorisations",
  "authors": [
    "Kiran Luecke"
  ],
  "comment": "Appendix (by Constantin Teleman) to appear in final version",
  "categories": [
    "math.RT"
  ],
  "abstract": "(With an Appendix by Constantin Teleman) In the spirit of Freed, Hopkins, and Teleman I establish an equivalence between the category of discrete series representations of a real semisimple Lie group G and a category of equivariant matrix factorisations on a subset of the dual of the Lie algebra, in analogy with the situation in [FT] which treated the case when G is compact or a loop group thereof. The equivalence is implemented by a version of the Dirac operator used in [FHT1-3], squaring to the superpotential W defining the matrix factorisations. Using the structure of the resulting matrix factorisation category as developed in [FT] I deduce the Kirillov character formula for compact Lie groups and the Rossman character formula for the discrete series of a real semi-simple Lie group. The proofs are a calculation of Chern characters and use the Dirac family constructed in [FHT1-3]. Indeed, the main theorems of [FHT3] and [FT] are a categorification of the Kirillov correspondence, and this paper establishes that this correspondence can be recovered at the level of characters.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-01T00:38:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "real semisimple lie group",
      "real semi-simple lie group",
      "equivariant matrix factorisations",
      "loop group thereof",
      "discrete series representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}