{
  "id": "2106.05028",
  "version": "v1",
  "published": "2021-06-09T12:39:01.000Z",
  "updated": "2021-06-09T12:39:01.000Z",
  "title": "On a convexity property of tensor products of irreducible, rational representations of $SL(n)$",
  "authors": [
    "Hariharan Narayanan",
    "C. S. Rajan"
  ],
  "comment": "5 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "The aim of this note is to point out a convexity property with respect to the root lattice for the support of the highest weights that occur in a tensor product of irreducible rational representations of $SL(n)$ over the complex numbers. The observation is a consequence of the convexity properties of the saturation cone and the validity of the saturation conjecture for $SL(n)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-09T12:39:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G05",
      "22E45",
      "05E10"
    ],
    "keywords": [
      "convexity property",
      "tensor product",
      "complex numbers",
      "irreducible rational representations",
      "root lattice"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}