{
  "id": "2403.13953",
  "version": "v1",
  "published": "2024-03-20T19:50:38.000Z",
  "updated": "2024-03-20T19:50:38.000Z",
  "title": "Commuting Varieties of Upper Triangular Matrices and Representation Homology",
  "authors": [
    "Guanyu Li"
  ],
  "categories": [
    "math.AG",
    "math.AC",
    "math.AT"
  ],
  "abstract": "We establish a connection between commuting varieties $C_g(G)$ (potentially of higher genus), which are associated with a group scheme $G$ consisting of upper triangular matrices, and the representation homology $HR_*(\\Sigma_g,G)$ of a Riemann surface $\\Sigma_g$ with coefficients in the group $G$. As an outcome, we provide a numerical criterion for determining whether commuting varieties $C(U_n)$ form a complete intersection for groups consisting of upper triangular unipotent matrices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-20T19:50:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14A30",
      "14M10",
      "55N35"
    ],
    "keywords": [
      "upper triangular matrices",
      "commuting varieties",
      "representation homology",
      "upper triangular unipotent matrices",
      "group scheme"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}