Maximally reducible monodromy of bivariate hypergeometric systems
IZVESTIYA MATHEMATICS, vol.80, no.1, pp.221-262, 2016 (SCI-Expanded, Scopus)
- 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
- Open Archive Collection: AVESIS Open Access Collection
- 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.