{
  "id": "0905.2395",
  "version": "v1",
  "published": "2009-05-14T18:42:09.000Z",
  "updated": "2009-05-14T18:42:09.000Z",
  "title": "On Discretization of Tori of Compact Simple Lie Groups",
  "authors": [
    "Jiri Hrivnak",
    "Jiri Patera"
  ],
  "comment": "22 pages, 6 figures",
  "journal": "J. Phys. A: Math. Theor. 42 (2009) 385208.",
  "doi": "10.1088/1751-8113/42/38/385208",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "Three types of numerical data are provided for simple Lie groups of any type and rank. This data is indispensable for Fourier-like expansions of multidimensional digital data into finite series of $C-$ or $S-$functions on the fundamental domain $F$ of the underlying Lie group $G$. Firstly, we consider the number $|F_M|$ of points in $F$ 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 $\\Lambda_M$ of dominant weights, specifying the maximal set of $C-$ and $S-$functions that are pairwise orthogonal on the point set $F_M$. Finally, we describe an efficient algorithm for finding, on the maximal torus of $G$, the number of conjugate points to every point of $F_M$. Discrete $C-$ and $S-$transforms, together with their continuous interpolations, are presented in full generality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-05-14T18:42:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "compact simple lie groups",
      "discretization",
      "dual weight lattice",
      "multidimensional digital data",
      "full generality"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2009,
      "month": "Sep",
      "volume": 42,
      "number": 38,
      "pages": 385208
    },
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009JPhA...42L5208H"
    }
  }
}