Maximally reducible monodromy of bivariate hypergeometric systems

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Sadykov T. M. , TANABE S.

IZVESTIYA MATHEMATICS, vol.80, no.1, pp.221-262, 2016 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 80 Issue: 1
  • Publication Date: 2016
  • Doi Number: 10.1070/im8211
  • Title of Journal : IZVESTIYA MATHEMATICS
  • Page Numbers: pp.221-262


We investigate the branching of solutions of holonomic bivariate Horn-type hypergeometric systems. Special attention is paid to invariant subspaces of Puiseux polynomial solutions. We mainly study Horn systems defined by simplicial configurations and Horn systems whose Ore-Sato polygons are either zonotopes or Minkowski sums of a triangle and segments proportional to its sides. We prove a necessary and sufficient condition for the monodromy representation to be maximally reducible, that is, for the space of holomorphic solutions to split into a direct sum of one-dimensional invariant subspaces.