{
  "id": "2108.00235",
  "version": "v1",
  "published": "2021-07-31T13:14:56.000Z",
  "updated": "2021-07-31T13:14:56.000Z",
  "title": "Thomae's function on a Lie group",
  "authors": [
    "Mark Reeder"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $\\mathfrak g$ be a simple complex Lie algebra of finite dimension. This paper gives an inequality relating the order of an automorphism of $\\mathfrak g$ to the dimension of its fixed-point subalgebra, and characterizes those automorphisms of $\\mathfrak g$ for which equality occurs. This is amounts to an inequality/equality for Thomae's function on the group of automorphisms of $\\mathfrak g$. The result has applications to characters of zero weight spaces, graded Lie algebras, and inequalities for adjoint Swan conductors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-31T13:14:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E10"
    ],
    "keywords": [
      "thomaes function",
      "lie group",
      "simple complex lie algebra",
      "automorphism",
      "adjoint swan conductors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}