{
  "id": "1512.04254",
  "version": "v1",
  "published": "2015-12-14T11:06:04.000Z",
  "updated": "2015-12-14T11:06:04.000Z",
  "title": "Involutions on the affine Grassmannian and moduli spaces of principal bundles",
  "authors": [
    "Anthony Henderson"
  ],
  "comment": "35 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $G$ be a connected reductive group over $\\mathbb{C}$. We show that a certain involution of an open subset of the affine Grassmannian of $G$, defined previously by Achar and the author, corresponds to the action of the nontrivial Weyl group element of $\\mathrm{SL}(2)$ on the framed moduli space of $\\mathbb{G}_m$-equivariant principal $G$-bundles on $\\mathbb{P}^2$. As a result, the fixed-point set of the involution can be partitioned into strata indexed by conjugacy classes of homomorphisms $N\\to G$ where $N$ is the normalizer of $\\mathbb{G}_m$ in $\\mathrm{SL}(2)$. In the case where $G=\\mathrm{GL}(r)$, the strata are Nakajima quiver varieties $\\mathfrak{M}_0^{\\mathrm{reg}}(\\mathbf{v},\\mathbf{w})$ of type D.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-14T11:06:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J60",
      "14M15",
      "17B08"
    ],
    "keywords": [
      "affine grassmannian",
      "principal bundles",
      "involution",
      "nontrivial weyl group element",
      "nakajima quiver varieties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}