{
  "id": "0804.0046",
  "version": "v1",
  "published": "2008-04-01T00:10:25.000Z",
  "updated": "2008-04-01T00:10:25.000Z",
  "title": "Trigonometric Cherednik algebra at critical level and quantum many-body problems",
  "authors": [
    "E. Emsiz",
    "E. M. Opdam",
    "J. V. Stokman"
  ],
  "comment": "31 pages",
  "journal": "Sel. math., New ser. 14 (2009), 571-605",
  "doi": "10.1007/s00029-009-0516-y",
  "categories": [
    "math.RT"
  ],
  "abstract": "For any module over the affine Weyl group we construct a representation of the associated trigonometric Cherednik algebra $A(k)$ at critical level in terms of Dunkl type operators. Under this representation the center of $A(k)$ produces quantum conserved integrals for root system generalizations of quantum spin-particle systems on the circle with delta function interactions. This enables us to translate the spectral problem of such a quantum spin-particle system to questions in the representation theory of $A(k)$. We use this approach to derive the associated Bethe ansatz equations. They are expressed in terms of the normalized intertwiners of $A(k)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-04-01T00:10:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C08",
      "81R12"
    ],
    "keywords": [
      "trigonometric cherednik algebra",
      "quantum many-body problems",
      "critical level",
      "quantum spin-particle system",
      "produces quantum conserved integrals"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0804.0046E"
    }
  }
}