{
  "id": "2308.06249",
  "version": "v1",
  "published": "2023-08-11T17:32:02.000Z",
  "updated": "2023-08-11T17:32:02.000Z",
  "title": "Characteristic cycles of IH sheaves of simply laced minuscule Schubert varieties are irreducible",
  "authors": [
    "Leonardo C. Mihalcea",
    "Rahul Singh"
  ],
  "comment": "14 pages, comments welcome!",
  "categories": [
    "math.AG",
    "math.RT"
  ],
  "abstract": "Let $G/P$ be a complex cominuscule flag manifold of type $E_6,E_7$. We prove that each characteristic cycle of the intersection homology (IH) complex of a Schubert variety in $G/P$ is irreducible. The proof utilizes an earlier algorithm by the same authors which calculates local Euler obstructions, then proceeds by direct computer calculation using Sage. This completes to the exceptional Lie types the characterization of irreducibility of IH sheaves of Schubert varieties in cominuscule $G/P$ obtained by Boe and Fu. As a by-product, we also obtain that the Mather classes, and the Chern-Schwartz-MacPherson classes of Schubert cells in cominuscule $G/P$ of type $E_6,E_7$, are strongly positive.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-11T17:32:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C17",
      "14M15",
      "32S60"
    ],
    "keywords": [
      "schubert variety",
      "simply laced minuscule schubert varieties",
      "characteristic cycle",
      "ih sheaves",
      "complex cominuscule flag manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}