{
  "id": "math/9810087",
  "version": "v1",
  "published": "1998-10-14T17:21:16.000Z",
  "updated": "1998-10-14T17:21:16.000Z",
  "title": "Remarks on critical points of phase functions and norms of Bethe vectors",
  "authors": [
    "Evgeny Mukhin",
    "Alexander Varchenko"
  ],
  "categories": [
    "math.RT",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider a tensor product of a Verma module and the linear representation of $sl(n+1)$. We prove that the corresponding phase function, which is used in the solutions of the KZ equation with values in the tensor product, has a unique critical point and show that the Hessian of the logarithm of the phase function at this critical point equals the Shapovalov norm of the corresponding Bethe vector.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-10-14T17:21:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "tensor product",
      "critical point equals",
      "kz equation",
      "linear representation",
      "unique critical point"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math.....10087M"
    }
  }
}