{
  "id": "1810.04293",
  "version": "v1",
  "published": "2018-10-09T23:03:59.000Z",
  "updated": "2018-10-09T23:03:59.000Z",
  "title": "Towards geometric Satake correspondence for Kac-Moody algebras -- Cherkis bow varieties and affine Lie algebras of type $A$",
  "authors": [
    "Hiraku Nakajima"
  ],
  "comment": "38 pages",
  "categories": [
    "math.RT",
    "hep-th",
    "math-ph",
    "math.MP",
    "math.QA"
  ],
  "abstract": "We give a provisional construction of the Kac-Moody Lie algebra module structure on the hyperbolic restriction of the intersection cohomology complex of the Coulomb branch of a framed quiver gauge theory, as a refinement of the conjectural geometric Satake correspondence for Kac-Moody algebras proposed in arXiv:1604.03625. This construction assumes several geometric properties of the Coulomb branch under the torus action. These properties are checked in affine type A, via the identification of the Coulomb branch with a Cherkis bow variety established in arXiv:1606.02002.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-09T23:03:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "geometric satake correspondence",
      "cherkis bow variety",
      "affine lie algebras",
      "kac-moody algebras",
      "coulomb branch"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}