{
  "id": "math/0610159",
  "version": "v3",
  "published": "2006-10-05T01:20:10.000Z",
  "updated": "2010-09-17T04:29:19.000Z",
  "title": "Generic Hecke Algebras for Monomial Groups",
  "authors": [
    "S. I. Alhaddad",
    "J. M. Douglass"
  ],
  "comment": "25 pages; This is a substantive revision. A construction of a Kazhdan-Lusztig C basis and Kazhdan-Lusztig polynomials for H was added. A lot of typos were fixed. Some new typos might have been introduced",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "In this paper we define a two-variable, generic Hecke algebra, H, for each complex reflection group G(b,1,n). The algebra H specializes to the group algebra of G(b,1,n) and also to an endomorphism algebra of a representation of GL(n,q) induced from a solvable subgroup. We construct Kazhdan-Lusztig \"R-polynomials\" for H and show that they may be used to define a partial order on G(b,1,n). Using a generalization of Deodhar's notion of distinguished subexpressions we give a closed formula for the R-polynomials. After passing to a one-variable quotient of the ring of scalars, we construct Kazhdan-Lusztig polynomials for H that reduce to the usual Kazhdan-Lusztig polynomials for the symmetric group when b=1.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-09-17T04:29:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C08"
    ],
    "keywords": [
      "generic hecke algebra",
      "monomial groups",
      "usual kazhdan-lusztig polynomials",
      "construct kazhdan-lusztig polynomials",
      "complex reflection group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....10159A"
    }
  }
}