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 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 80 Issue: 1
  • Publication Date: 2016
  • Doi Number: 10.1070/im8211
  • Journal Name: IZVESTIYA MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.221-262
  • Galatasaray University Affiliated: Yes

Abstract

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.