{
  "id": "1407.8423",
  "version": "v1",
  "published": "2014-07-31T14:07:24.000Z",
  "updated": "2014-07-31T14:07:24.000Z",
  "title": "A path model for Whittaker vectors",
  "authors": [
    "P. Di Francesco",
    "R. Kedem",
    "B. Turmunkh"
  ],
  "comment": "40 pages, 2 figures",
  "categories": [
    "math.RT",
    "math-ph",
    "math.MP",
    "math.QA"
  ],
  "abstract": "In this paper we construct weighted path models to compute Whittaker vectors in the completion of Verma modules, as well as Whittaker functions of fundamental type, for all finite-dimensional simple Lie algebras, affine Lie algebras, and the quantum algebra $U_q(\\mathfrak{sl}_{r+1})$. This leads to series expressions for the Whittaker functions. We show how this construction leads directly to the quantum Toda equations satisfied by these functions, and to the $q$-difference equations in the quantum case. We investigate the critical limit of affine Whittaker functions computed in this way.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-31T14:07:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "whittaker vectors",
      "finite-dimensional simple lie algebras",
      "affine whittaker functions",
      "construct weighted path models",
      "affine lie algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1309214,
      "adsabs": "2014arXiv1407.8423D"
    }
  }
}