{
  "id": "2309.07279",
  "version": "v1",
  "published": "2023-09-13T19:56:39.000Z",
  "updated": "2023-09-13T19:56:39.000Z",
  "title": "Levi-Equivariant Restriction of Spherical Perverse Sheaves",
  "authors": [
    "Mark Macerato"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "We study the equivariant cohomology of spherical perverse sheaves on the affine Grassmannian of a connected reductive group $G$ with support in the affine Grassmannian of any Levi subgroup $L$ of $G$. In doing so, we extend the work of Ginzburg and Riche on the $T$-equivariant cofibers of spherical perverse sheaves. We obtain a description of this cohomology in terms of the Langlands dual group $\\check{G}$. More precisely, we identify the cohomology of the regular sheaf on $\\mathrm{Gr}_G$ with support along $\\mathrm{Gr}_L$ with the algebra of functions on a hyperspherical Hamiltonian $\\check{G}$-variety $T^*(\\check{G}/(\\check{U}, \\psi_L))$, where the $\\textit{Whittaker datum}$ $\\psi_L$ is an additive character (determined by $L$) of the maximal unipotent subgroup $\\check{U}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-13T19:56:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spherical perverse sheaves",
      "levi-equivariant restriction",
      "affine grassmannian",
      "maximal unipotent subgroup",
      "langlands dual group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}