{
  "id": "1412.7408",
  "version": "v1",
  "published": "2014-12-23T15:40:44.000Z",
  "updated": "2014-12-23T15:40:44.000Z",
  "title": "The Kazhdan-Lusztig polynomial of a matroid",
  "authors": [
    "Ben Elias",
    "Nicholas Proudfoot",
    "Max Wakefield"
  ],
  "comment": "34 pages",
  "categories": [
    "math.CO",
    "math.AG",
    "math.RT"
  ],
  "abstract": "We associate to every matroid M a polynomial with integer coefficients, which we call the Kazhdan-Lusztig polynomial of M, in analogy with Kazhdan-Lusztig polynomials in representation theory. We conjecture that the coefficients are always non-negative, and we prove this conjecture for representable matroids by interpreting our polynomials as intersection cohomology Poincare polynomials. We also introduce a q-deformation of the Mobius algebra of M, and use our polynomials to define a special basis for this deformation, analogous to the canonical basis of the Hecke algebra. We conjecture that the structure coefficients for multiplication in this special basis are non-negative, and we verify this conjecture in numerous examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-23T15:40:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B35",
      "14F43",
      "52C35"
    ],
    "keywords": [
      "kazhdan-lusztig polynomial",
      "special basis",
      "intersection cohomology poincare polynomials",
      "conjecture",
      "mobius algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.7408E"
    }
  }
}