{
  "id": "2103.13594",
  "version": "v1",
  "published": "2021-03-25T03:57:57.000Z",
  "updated": "2021-03-25T03:57:57.000Z",
  "title": "Parabolic induction and the Harish-Chandra D-module",
  "authors": [
    "Victor Ginzburg"
  ],
  "comment": "12pp",
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "Let G be a reductive group and L a Levi subgroup. Parabolic induction and restriction are a pair of adjoint functors between Ad-equivariant derived categories of either constructible sheaves or (not necessarily holonomic) D-modules on G and L, respectively. Bezrukavnikov and Yom Din proved, generalizing a classic result of Lusztig, that these functors are exact. In this paper, we consider a special case where L=T is a maximal torus. We give explicit formulas for parabolic induction and restriction in terms of the Harish-Chandra module D-module on G x T. We show that this module is flat over D(T), which easily implies that parabolic induction and restriction are exact functors between the corresponding abelian categories of D-modules.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-25T03:57:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "parabolic induction",
      "harish-chandra d-module",
      "restriction",
      "harish-chandra module d-module",
      "levi subgroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}