{
  "id": "2103.02168",
  "version": "v1",
  "published": "2021-03-03T04:23:51.000Z",
  "updated": "2021-03-03T04:23:51.000Z",
  "title": "Symmetric permutation invariants in some tensor products",
  "authors": [
    "Zhipeng Lu"
  ],
  "comment": "All comments are welcome",
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "This is a note for constructing fundamental invariants and computing the Hilbert series of the invariant subalgebras of tensor products of polynomial rings under the action by a direct product of symmetric groups. Our computation relies on Schur functions bringing together several identities of combinatorial generating functions including that of plane partitions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-03T04:23:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C30",
      "20C15",
      "05A19"
    ],
    "keywords": [
      "symmetric permutation invariants",
      "tensor products",
      "plane partitions",
      "constructing fundamental invariants",
      "polynomial rings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}