Maximally reducible monodromy of bivariate hypergeometric systems


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Sadykov T. M. , TANABE S.

IZVESTIYA MATHEMATICS, cilt.80, ss.221-262, 2016 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 80 Konu: 1
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1070/im8211
  • Dergi Adı: IZVESTIYA MATHEMATICS
  • Sayfa Sayıları: ss.221-262

Özet

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.