{
  "id": "2102.01849",
  "version": "v1",
  "published": "2021-02-03T03:04:06.000Z",
  "updated": "2021-02-03T03:04:06.000Z",
  "title": "Invariant theory for the commuting scheme of symplectic Lie algebras",
  "authors": [
    "Tsao-Hsien Chen",
    "Ngo Bao Chau"
  ],
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "We prove the Chevalley restriction theorem for the commuting scheme of symplectic Lie algebras. The key step is the construction of the inverse map of the Chevalley restriction map called the spectral data map. Along the way, we establish a certain multiplicative property of the Pfaffian which is of independent interest.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-03T03:04:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symplectic lie algebras",
      "commuting scheme",
      "invariant theory",
      "chevalley restriction theorem",
      "chevalley restriction map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}