Global analysis of GG systems

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 functions meromorphic and periodic with respect to a lattice. We describe the monodromy invariant subspace of the solution space. We give a connection formula between a pair of bases consisting of $\mathrm{\Gamma }$-series solutions of GG system associated to a pair of regular triangulations adjacent to each other in the secondary fan.