Global Analysis of GG Systems

Abstract

Abstract This paper deals with some analytic aspects of GG system introduced by I.M. Gelfand and M.I. Graev: we compute the dimension of the solution space of GG system over the field of meromorphic functions periodic with respect to a lattice. We describe the monodromy invariant subspace of the solution space. We provide a connection formula between a pair of bases consisting of $\Gamma $-series solutions of GG system associated with a pair of regular triangulations adjacent to each other in the secondary fan.