{
  "id": "2210.14729",
  "version": "v1",
  "published": "2022-10-26T14:02:49.000Z",
  "updated": "2022-10-26T14:02:49.000Z",
  "title": "Unitary monodromies for rank two Fuchsian systems with $(n+1)$ singularities",
  "authors": [
    "Shunya Adachi"
  ],
  "comment": "20 pages, 1 figure",
  "categories": [
    "math.CA"
  ],
  "abstract": "We study the unitarity of monodromies for rank two Fuchsian systems of SL type with $(n+1)$ regular singularities on the Riemann sphere, namely, we give a sufficient and necessary condition for the monodromy group to be conjugate to a subgroup of a special unitary group $\\mathrm{SU}(p,q)$. When $n\\ge 3$, the moduli space of irreducible monodromies can be realized as an affine algebraic set in $\\mathbb{C}^m$ for some $m \\in \\mathbb{N}$. In this paper we give a characterization and construction of unitary monodromies in terms of this affine algebraic set. The criterion of the signatures of unitary monodromies is also given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-26T14:02:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34M35",
      "34M15"
    ],
    "keywords": [
      "unitary monodromies",
      "fuchsian systems",
      "affine algebraic set",
      "special unitary group",
      "regular singularities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}