{
  "id": "1503.06510",
  "version": "v2",
  "published": "2015-03-23T02:32:27.000Z",
  "updated": "2015-04-10T15:18:28.000Z",
  "title": "Local Weyl modules and cyclicity of tensor products for Yangians",
  "authors": [
    "Yilan Tan",
    "Nicolas Guay"
  ],
  "comment": "26 pages",
  "journal": "Journal of Algebra, 432(2015), 228-251",
  "doi": "10.1016/j.jalgebra.2015.02.023",
  "categories": [
    "math.RT"
  ],
  "abstract": "We provide a sufficient condition for the cyclicity of an ordered tensor product $L=V_{a_1}(\\omega_{b_1})\\otimes V_{a_2}(\\omega_{b_2})\\otimes...\\otimes V_{a_k}(\\omega_{b_k})$ of fundamental representations of the Yangian $Y(\\mathfrak{g})$. When $\\mathfrak{g}$ is a classical simple Lie algebra, we make the cyclicity condition concrete, which leads to an irreducibility criterion for the ordered tensor product $L$. In the case when $\\mathfrak{g}=\\mathfrak{sl}_{l+1}$, a sufficient and necessary condition for the irreducibility of the ordered tensor product $L$ is obtained. The cyclicity of the ordered tensor product $L$ is closely related to the structure of the local Weyl modules of $Y(\\mathfrak{g})$. We show that every local Weyl module is isomorphic to an ordered tensor product of fundamental representations of $Y(\\mathfrak{g})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-23T02:32:27.000Z",
      "abstract": "We provide a sufficient condition for the cyclicity of an ordered tensor product $L=V_{a_1}(\\omega_{b_1})\\otimes V_{a_2}(\\omega_{b_2})\\otimes\\ldots\\otimes V_{a_k}(\\omega_{b_k})$ of fundamental representations of the Yangian $Y(\\mathfrak{g})$. When $\\mathfrak{g}$ is a classical simple Lie algebra, we make the cyclicity condition concrete, which leads to an irreducibility criterion for the ordered tensor product $L$. In the case when $\\mathfrak{g}=\\mathfrak{sl}_{l+1}$, a sufficient and necessary condition for the irreducibility of the ordered tensor product $L$ is obtained. The cyclicity of the ordered tensor product $L$ is closely related to the structure of the local Weyl modules of $Y(\\mathfrak{g})$. We show that every local Weyl module is isomorphic to an ordered tensor product of fundamental representations of $Y(\\mathfrak{g})$.",
      "journal": null
    },
    {
      "version": "v2",
      "updated": "2015-04-10T15:18:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G42",
      "81R50"
    ],
    "keywords": [
      "local weyl module",
      "ordered tensor product",
      "fundamental representations",
      "classical simple lie algebra",
      "cyclicity condition concrete"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150306510T"
    }
  }
}