{
  "id": "math/9806140",
  "version": "v1",
  "published": "1998-06-25T09:18:44.000Z",
  "updated": "1998-06-25T09:18:44.000Z",
  "title": "Infinite dimensional geometry of $M_1=Diff_+(S^1)/PSL(2,R)$ and $q_R$--conformal symmetries",
  "authors": [
    "Denis V. Juriev"
  ],
  "comment": "14 pp, AMSTEX",
  "categories": [
    "math.RT",
    "math.DG",
    "math.QA"
  ],
  "abstract": "A geometric interpretation of approximate ($HS$-projective or $TC$-projective) representations of the Witt algebra $w^C$ by $q_R$-conformal symmetries in the Verma modules $V_h$ over the Lie algebra $sl(2,C)$ is established and some their characteristics are calculated. It is shown that the generators of representations coincide with the Nomizu operators of holomorphic $w^C$-invariant hermitean connections in the deformed holomorphic tangent bundles $T_h(M_1)$ over the infinite-dimensional K\\\"ahler manifold $M_1=\\Diff_+(S^1)/PSL(2,R)$, whereas the deviations $A_{XY}$ of the approximate representations coincide with the curvature operators for these connections, which supply the determinant bundle $det T_h(M_1)$ by a structure of the prequantization bundle over $M_1$. At $h=2$ the geometric picture reduces to one considered by A.A.Kirillov and the author [Funct.Anal.Appl. 21(4) (1987) 284-293] (without any relation to the approximate representations) for ordinary tangent bundles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-06-25T09:18:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "infinite dimensional geometry",
      "conformal symmetries",
      "ordinary tangent bundles",
      "approximate representations coincide",
      "deformed holomorphic tangent bundles"
    ],
    "note": {
      "typesetting": "AMS-TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math......6140J"
    }
  }
}