{
  "id": "2406.03238",
  "version": "v1",
  "published": "2024-06-05T13:16:44.000Z",
  "updated": "2024-06-05T13:16:44.000Z",
  "title": "The parity of Lusztig's restriction functor and Green's formula for a quiver with automorphism",
  "authors": [
    "Jiepeng Fang",
    "Yixin Lan",
    "Yumeng Wu"
  ],
  "categories": [
    "math.RT",
    "math.QA",
    "math.RA"
  ],
  "abstract": "In [8], Fang-Lan-Xiao proved a formula about Lusztig's induction and restriction functors which can induce Green's formula for the path algebra of a quiver over a finite field via the trace map. In this paper, we generalize their formula to that for the mixed semisimple perverse sheaves for a quiver with an automorphism. By applying the trace map, we obtain Green's formula for any finite-dimensional hereditary algebra over a finite field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-05T13:16:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "17B37"
    ],
    "keywords": [
      "lusztigs restriction functor",
      "automorphism",
      "trace map",
      "finite field",
      "induce greens formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}