TL;DR
This paper analyzes the GG system, focusing on solution space dimensions, monodromy invariants, and connection formulas between bases, advancing understanding of its analytic and algebraic properties.
Contribution
It provides explicit computations of solution space dimensions, describes monodromy invariants, and establishes connection formulas between different bases of solutions.
Findings
Dimension of solution space computed
Monodromy invariant subspace characterized
Connection formulas between bases derived
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 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 -series solutions of GG system associated to a pair of regular triangulations adjacent to each other in the secondary fan.
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