{
  "id": "0912.4194",
  "version": "v2",
  "published": "2009-12-21T20:14:35.000Z",
  "updated": "2010-04-01T13:05:29.000Z",
  "title": "On E-Discretization of Tori of Compact Simple Lie Groups",
  "authors": [
    "Jiří Hrivnák",
    "Jiří Patera"
  ],
  "comment": "13 pages, 2 figures, revised version",
  "journal": "J. Phys. A: Math. Theor. 43 (2010) 165206",
  "doi": "10.1088/1751-8113/43/16/165206",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "Three types of numerical data are provided for compact simple Lie groups $G$ of classical types and of any rank. This data is indispensable for Fourier-like expansions of multidimensional digital data into finite series of $E-$functions on the fundamental domain $F^{e}$. Firstly, we determine the number $|F^{e}_M|$ of points in $F^{e}$ from the lattice $P^{\\vee}_M$, which is the refinement of the dual weight lattice $P^{\\vee}$ of $G$ by a positive integer $M$. Secondly, we find the lowest set $\\Lambda^{e}_M$ of the weights, specifying the maximal set of $E-$functions that are pairwise orthogonal on the point set $F^{e}_M$. Finally, we describe an efficient algorithm for finding the number of conjugate points to every point of $F^{e}_M$. Discrete $E-$transform, together with its continuous interpolation, is presented in full generality.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-04-01T13:05:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "compact simple lie groups",
      "e-discretization",
      "multidimensional digital data",
      "dual weight lattice",
      "full generality"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2010,
      "month": "Apr",
      "volume": 43,
      "number": 16,
      "pages": 165206
    },
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010JPhA...43p5206H"
    }
  }
}