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We investigate branching of solutions to holonomic bivariate hypergeometricsystems of Horn's type. Special attention is paid to the invariant subspace ofPuiseux polynomial solutions. We mainly study Horn systems defined bysimplicial configurations and Horn systems whose Ore-Sato polygons are eitherzonotopes or Minkowski sums of a triangle and segments proportional to itssides. We prove a necessary and sufficient condition for the monodromyrepresentation to be maximally reducible, that is, for the space of holomorphicsolutions to split into the direct sum of one-dimensional invariant subspaces.

Maximally reducible monodromy of bivariate hypergeometric systems