{
  "id": "2212.14496",
  "version": "v1",
  "published": "2022-12-30T00:36:20.000Z",
  "updated": "2022-12-30T00:36:20.000Z",
  "title": "Construction of the traceless projection of tensors via the Brauer algebra",
  "authors": [
    "D. V. Bulgakova",
    "Y. O. Goncharov",
    "T. Helpin"
  ],
  "comment": "42 pages",
  "categories": [
    "math.RT",
    "hep-th",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We describe how traceless projection of tensors of a given rank can be constructed in a closed form. On the way to this goal we invoke the representation theory of the Brauer algebra and the related Schur-Weyl dualities. The resulting traceless projector is constructed from purely combinatorial data involving Young diagrams. By construction, the projector manifestly commutes with the symmetric group and is well-adapted to restrictions to $GL$-irreducible tensor representations. We develop auxiliary computational techniques which serve to take advantage of the obtained results for applications. The proposed method of constructing traceless projectors leads to a particular central idempotent in the semisimple regime of the Brauer algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-30T00:36:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "brauer algebra",
      "traceless projection",
      "construction",
      "auxiliary computational techniques",
      "traceless projector"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}