{
  "id": "2411.00675",
  "version": "v1",
  "published": "2024-11-01T15:34:56.000Z",
  "updated": "2024-11-01T15:34:56.000Z",
  "title": "On integral $\\mathrm{Ext^2}$ between certain Weyl modules of $\\mathrm{GLn}$",
  "authors": [
    "Maria Metzaki"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Consider partitions of the form $\\lambda=(a,1^b)$ and $\\mu=(a+1,b-1)$,\\\\ where $a+1>b-1$. In this paper, we determine the extension groups $\\mathrm{Ext}_A^2(K_{\\lambda}F,K_{\\mu}F)$, where $F$ is a free $\\mathbb{Z}-$module of finite rank $n$, $K_{\\lambda}F$ and $K_{\\mu}F$ are the Weyl modules of the general linear group $GL_n(\\mathbb{Z})$ corresponding to $\\lambda$ and $\\mu$, respectively, $A=S_\\mathbb{Z}(n,r)$ is the integral Schur algebra and $r=a+b$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-01T15:34:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G05"
    ],
    "keywords": [
      "weyl modules",
      "integral schur algebra",
      "general linear group",
      "extension groups",
      "finite rank"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}