{
  "id": "1809.05601",
  "version": "v1",
  "published": "2018-09-14T21:52:38.000Z",
  "updated": "2018-09-14T21:52:38.000Z",
  "title": "Limit shape of probability measure on tensor product of $B_n$ algebra modules",
  "authors": [
    "Anton Nazarov",
    "Olga Postnova"
  ],
  "comment": "Submitted to Zapiski Nauchnykh Seminarov POMI",
  "categories": [
    "math.RT",
    "math.PR"
  ],
  "abstract": "We study a probability measure on integral dominant weights in the decomposition of $N$-th tensor power of spinor representation of the Lie algebra $so(2n+1)$. The probability of the dominant weight $\\lambda$ is defined as the ratio of the dimension of the irreducible component of $\\lambda$ divided by the total dimension $2^{nN}$ of the tensor power. We prove that as $N\\to \\infty$ the measure weakly converges to the radial part of the $SO(2n+1)$-invariant measure on $so(2n+1)$ induced by the Killing form. Thus, we generalize Kerov's theorem for $su(n)$ to $so(2n+1)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-14T21:52:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B10",
      "17B10"
    ],
    "keywords": [
      "probability measure",
      "tensor product",
      "algebra modules",
      "limit shape",
      "integral dominant weights"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}