Galois theory of fuchsian q-difference equations

Abstract

We propose an analytical approach to the Galois theory of singular regular linear q-difference systems. We use Tannaka duality along with Birkhoff's classification scheme with the connection matrix to define and describe their Galois groups. Then we describe fundamental subgroups that give rise to a Riemann–Hilbert correspondence and to a density theorem of Schlesinger's type.