{
  "id": "math/0202182",
  "version": "v1",
  "published": "2002-02-18T19:33:04.000Z",
  "updated": "2002-02-18T19:33:04.000Z",
  "title": "Enveloping algebra U(gl(3)) and orthogonal polynomials in several discrete indeterminates",
  "authors": [
    "Alexander Sergeev"
  ],
  "comment": "12p., Latex",
  "journal": "Duplij S., Wess J. (eds.) Noncommutative structures in mathematics and physics, Proc. NATO Advanced Research Workshop, Kiev, 2000. Kluwer, 2001, 113--124",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let A be an associative complex algebra and L an invariant linear functional on it (trace). Let i be an involutive antiautomorphism of A such that L(i(a))=L(a) for any a in A. Then A admits a symmetric invariant bilinear form (a, b)=L(a i(b)). For A=U(sl(2))/m, where m is any maximal ideal of U(sl(2)), Leites and I have constructed orthogonal basis whose elements turned out to be, essentially, Chebyshev and Hahn polynomials in one discrete variable. Here I take A=U(gl(3))/m for the maximal ideals m which annihilate irreducible highest weight gl(3)-modules of particular form (generalizations of symmetric powers of the identity representation). In this way we obtain multivariable analogs of Hahn polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-02-18T19:33:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "17B65",
      "33C45",
      "33C80"
    ],
    "keywords": [
      "discrete indeterminates",
      "orthogonal polynomials",
      "enveloping algebra",
      "maximal ideal",
      "symmetric invariant bilinear form"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......2182S"
    }
  }
}