{
  "id": "1502.03511",
  "version": "v1",
  "published": "2015-02-12T02:14:51.000Z",
  "updated": "2015-02-12T02:14:51.000Z",
  "title": "Invariants of the vacuum module associated with the Lie superalgebra gl(1|1)",
  "authors": [
    "A. I. Molev",
    "E. E. Mukhin"
  ],
  "comment": "24 pages",
  "categories": [
    "math.RT",
    "math-ph",
    "math.CO",
    "math.MP"
  ],
  "abstract": "We describe the algebra of invariants of the vacuum module associated with the affinization of the Lie superalgebra $\\mathfrak{gl}(1|1)$. We give a formula for its Hilbert--Poincar\\'{e} series in a fermionic (cancellation-free) form which turns out to coincide with the generating function of the plane partitions over the $(1,1)$-hook. Our arguments are based on a super version of the Beilinson--Drinfeld--Ra\\\"{i}s--Tauvel theorem which we prove by producing an explicit basis of invariants of the symmetric algebra of polynomial currents associated with $\\mathfrak{gl}(1|1)$. We identify the invariants with affine supersymmetric polynomials via a version of the Chevalley theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-12T02:14:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "vacuum module",
      "lie superalgebra",
      "invariants",
      "affine supersymmetric polynomials",
      "chevalley theorem"
    ],
    "publication": {
      "doi": "10.1088/1751-8113/48/31/314001",
      "journal": "Journal of Physics A Mathematical General",
      "year": 2015,
      "month": "Aug",
      "volume": 48,
      "number": 31,
      "pages": 314001
    },
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015JPhA...48E4001M"
    }
  }
}