{
  "id": "2007.14512",
  "version": "v1",
  "published": "2020-07-28T22:45:14.000Z",
  "updated": "2020-07-28T22:45:14.000Z",
  "title": "Total nonnegativity and induced sign characters of the Hecke algebra",
  "authors": [
    "Adam Clearwater",
    "Mark Skandera"
  ],
  "comment": "24 pages",
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "Let $\\mathfrak S_{[i,j]}$ be the subgroup of the symmetric group $\\mathfrak S_n$ generated by adjacent transpositions $(i,i+1), \\dotsc, (j-1,j)$, assuming $1 \\leq i < j \\leq n$. We give a combinatorial rule for evaluating induced sign characters of the type-$A$ Hecke algebra $H_n(q)$ at all elements of the form $\\sum_{w \\in \\mathfrak S_{[i,j]}} T_w$ and at all products of such elements. This includes evaluation at some elements $C'_w(q)$ of the Kazhdan-Lusztig basis.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-28T22:45:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E15",
      "20C08"
    ],
    "keywords": [
      "hecke algebra",
      "total nonnegativity",
      "symmetric group",
      "adjacent transpositions",
      "combinatorial rule"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}