{
  "id": "1812.09791",
  "version": "v1",
  "published": "2018-12-23T22:50:04.000Z",
  "updated": "2018-12-23T22:50:04.000Z",
  "title": "Twisted De Rham complex on line and $\\widehat{frak{sl}_2}$ singular vectors",
  "authors": [
    "Alexey Slinkin",
    "Alexander Varchenko"
  ],
  "comment": "Latex, 29 pages",
  "categories": [
    "math.AG",
    "math-ph",
    "math.MP",
    "math.QA"
  ],
  "abstract": "We consider two complexes. The first complex is the twisted De Rham complex of scalar meromorphic differential forms on projective line, holomorphic on the complement to a finite set of points. The second complex is the chain complex of the Lie algebra of $\\frak{sl}_2$-valued algebraic functions on the same complement, with coefficients in a tensor product of contragradient dual Verma modules over the affine Lie algebra $\\widehat{frak{sl}_2}$. In [SV2] a construction of a monomorphism of the first complex to the second was suggested. It was indicated in [SV2] that under this monomorphism the existence of singular vectors in the Verma modules (the Malikov-Feigin-Fuchs singular vectors) is reflected in the relations between the cohomology classes of the De Rham complex. In this paper we prove the results formulated in [SV2].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-23T22:50:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rham complex",
      "first complex",
      "contragradient dual verma modules",
      "scalar meromorphic differential forms",
      "affine lie algebra"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}