{
  "id": "1801.06071",
  "version": "v1",
  "published": "2018-01-18T14:53:19.000Z",
  "updated": "2018-01-18T14:53:19.000Z",
  "title": "Quiver varieties and symmetric pairs",
  "authors": [
    "Yiqiang Li"
  ],
  "comment": "49 pages",
  "categories": [
    "math.RT",
    "math.SG"
  ],
  "abstract": "We study fixed-point loci of Nakajima varieties under symplectomorphisms and their anti-symplectic cousins, which are compositions of a diagram automorphism, a reflection functor and a transpose defined by certain bilinear forms. These subvarieties provide a natural home for geometric representation theory of symmetric pairs. In particular, the cohomology of a Steinberg-type variety of the symplectic fixed-point subvarieties is conjecturally related to the universal enveloping algebra of the subalgebra in a symmetric pair. The latter symplectic subvarieties are further used to construct geometrically an action of a twisted Yangian on torus equivariant cohomology of Nakajima varieties. In type $A$ case, these subvarieties provide a quiver model for partial Springer resolutions of nilpotent Slodowy slices of classical groups and associated symmetric spaces, which leads to a rectangular symmetry and a refinement of Kraft-Procesi row/column removal reductions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-18T14:53:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symmetric pair",
      "quiver varieties",
      "nakajima varieties",
      "kraft-procesi row/column removal reductions",
      "torus equivariant cohomology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 49,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}