{
  "id": "2001.11310",
  "version": "v1",
  "published": "2020-01-30T13:46:38.000Z",
  "updated": "2020-01-30T13:46:38.000Z",
  "title": "Complexity and Support Varieties for Type P Lie Superalgebras",
  "authors": [
    "Brian D. Boe",
    "Jonathan R. Kujawa"
  ],
  "comment": "26 pages, 22 figures. A companion iOS app, Homologica, is available on the Apple App Store",
  "categories": [
    "math.RT"
  ],
  "abstract": "We compute the complexity, z-complexity, and support varieties of the (thick) Kac modules for the Lie superalgebras of type P. We also show the complexity and the z-complexity have geometric interpretations in terms of support and associated varieties; these results are in agreement with formulas previously discovered for other classes of Lie superalgebras. Our main technical tool is a recursive algorithm for constructing projective resolutions for the Kac modules. The indecomposable projective summands which appear in a given degree of the resolution are explicitly described using the combinatorics of weight diagrams. Surprisingly, the number of indecomposable summands in each degree can be computed exactly: we give an explicit formula for the corresponding generating function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-30T13:46:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B55",
      "17B10",
      "17B56"
    ],
    "keywords": [
      "lie superalgebras",
      "support varieties",
      "kac modules",
      "z-complexity",
      "geometric interpretations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}