{
  "id": "2007.12638",
  "version": "v1",
  "published": "2020-07-24T16:45:54.000Z",
  "updated": "2020-07-24T16:45:54.000Z",
  "title": "Study of parity sheaves arising from graded Lie algebra",
  "authors": [
    "Tamanna Chatterjee"
  ],
  "comment": "39 pages. Comments are welcome!",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $G$ be a complex, connected, reductive, algebraic group, and $\\chi:\\mathbb{C}^\\times \\to G$ be a fixed cocharacter that defines a grading on $\\mathfrak{g}$, the Lie algebra of $G$. Let $G_0$ be the centralizer of $\\chi(\\mathbb{C}^\\times)$. In this paper, we study $G_0$-equivariant parity sheaves on $\\mathfrak{g}_n$, under some assumptions on the field $\\Bbbk$ and the group $G$. The assumption on $G$ holds for $GL_n$ and for any $G$, it recovers results of Lusztig in characteristic $0$. The main result is that every parity sheaf occurs as a direct summand of the parabolic induction of some cuspidal pair.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-24T16:45:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "20G05",
      "17B10"
    ],
    "keywords": [
      "graded lie algebra",
      "parity sheaves arising",
      "parity sheaf occurs",
      "equivariant parity sheaves",
      "algebraic group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}