{
  "id": "1502.04633",
  "version": "v1",
  "published": "2015-02-13T20:01:20.000Z",
  "updated": "2015-02-13T20:01:20.000Z",
  "title": "Evaluations of Hecke algebra traces at Kazhdan-Lusztig basis elements",
  "authors": [
    "Samuel Clearman",
    "Matthew Hyatt",
    "Brittany Shelton",
    "Mark Skandera"
  ],
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "For irreducible characters $\\{ \\chi_q^\\lambda \\,|\\, \\lambda \\vdash n \\}$, induced sign characters $\\{ \\epsilon_q^\\lambda \\,|\\, \\lambda \\vdash n \\}$, and induced trivial characters $\\{ \\eta_q^\\lambda \\,|\\, \\lambda \\vdash n \\}$ of the Hecke algebra $H_n(q)$, and Kazhdan-Lusztig basis elements $C'_w(q)$ with $w$ avoiding the patterns 3412 and 4231, we combinatorially interpret the polynomials $\\chi_q^\\lambda(q^{l(w)/2}C'_w(q))$, $\\epsilon_q^\\lambda(q^{l(w)/2} C'_w(q))$, and $\\smash{\\eta_q^\\lambda(q^{l(w)/2} C'_w(q))}$. This gives a new algebraic interpretation of chromatic quasisymmetric functions of Shareshian and Wachs, and a new combinatorial interpretation of special cases of results of Haiman. We prove similar results for other $H_n(q)$-traces, and confirm a formula conjectured by Haiman.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-13T20:01:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05",
      "05E10",
      "20C08"
    ],
    "keywords": [
      "kazhdan-lusztig basis elements",
      "hecke algebra traces",
      "evaluations",
      "chromatic quasisymmetric functions",
      "induced trivial characters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150204633C"
    }
  }
}